{"id":28473,"date":"2023-05-03T16:57:44","date_gmt":"2023-05-03T16:57:44","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=28473"},"modified":"2024-01-16T10:20:35","modified_gmt":"2024-01-16T10:20:35","slug":"linear-pair-of-angles-definition-axioms-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles","title":{"rendered":"Linear Pair of Angles: Definition, Axioms, Examples, Facts, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-6e92ef59-f1ae-40e4-9477-d931d0c82870\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles#0-what-is-a-linear-pair-of-angles>What Is a Linear Pair Of Angles?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles#2-properties-of-linear-pair-of-angles>Properties of Linear Pair of Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles#6-linear-pair-of-angles-vs-supplementary-angles>Linear Pair of Angles vs. Supplementary Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles#7-solved-examples-on-linear-pair-of-angles>Solved Examples on Linear Pair of Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles#8-practice-problems-on-linear-pair-of-angles>Practice Problems on Linear Pair of Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles#9-frequently-asked-questions-on-linear-pair-of-angles>Frequently Asked Questions on Linear Pair of Angles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-linear-pair-of-angles\">What Is a Linear Pair Of Angles?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>A linear pair of angles is a pair of adjacent angles formed when two lines intersect each other at a single point.<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u201cLinear\u201d simply means \u201carranged along a straight line.\u201d We know that a straight angle is an angle that measures $180^\\circ$. It is called a straight angle because it appears as a straight line. Two angles formed along a straight line represent a linear pair of angles.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/a-straight-angle-BOA.png\" alt=\"a straight angle BOA\" class=\"wp-image-34534\" title=\"a straight angle BOA\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/a-straight-angle-BOA.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/a-straight-angle-BOA-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the diagram shown below, $\\angle POA$ and $\\angle POB$ form a linear pair of angles. They add up to $180^\\circ$. In other words, they are supplementary.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle POA + \\angle POB = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Observe that these angles have one common arm (OP), which makes them adjacent angles. Also, their non-common sides OA and OB are opposite rays.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"419\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/a-linear-pair-of-angles.png\" alt=\"\" class=\"wp-image-34538\" title=\"a linear pair of angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/a-linear-pair-of-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/a-linear-pair-of-angles-300x203.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Examples of Linear Pair of Angles:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">1) In the figure given below, the linear pair of angles are:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle 1 ,\\; \\angle 4$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle 1 ,\\; \\angle 2$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle 3 ,\\; \\angle 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle 3,\\; \\angle 4$&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"315\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-of-angles-formed-by-two-intersecting-lines.png\" alt=\"linear pair of angles formed by two intersecting lines\" class=\"wp-image-34539\" title=\"linear pair of angles formed by two intersecting lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-of-angles-formed-by-two-intersecting-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-of-angles-formed-by-two-intersecting-lines-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">2) Here, $\\angle ADC$ and $\\angle BDC$ form a linear pair of angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"489\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-linear-pair-of-angles.png\" alt=\"example of linear pair of angles\" class=\"wp-image-34540\" title=\"example of linear pair of angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-linear-pair-of-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-of-linear-pair-of-angles-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-the-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_add_angles_pt.png\" alt=\"Add the Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add the Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-factor-pairs-for-a-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_complete_factor_pair_pt.png\" alt=\"Complete Factor Pairs for a Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete Factor Pairs for a Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-objects-in-linear-arrangement\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_hoppys_list_9_gm.png\" alt=\"Count Objects in Linear Arrangement Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Objects in Linear Arrangement Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-objects-in-non-linear-arrangement\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_hoppys_list_1_gm.png\" alt=\"Count Objects in Non-Linear Arrangement Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Objects in Non-Linear Arrangement Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-objects-in-non-linear-arrangement-within-10\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_hoppys_list_2_gm.png\" alt=\"Count Objects in Non-Linear Arrangement within 10 Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Objects in Non-Linear Arrangement within 10 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-objects-in-pairs\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_foundation_count_objects_in_pairs_pt.png\" alt=\"Count Objects in Pairs Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Objects in Pairs Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-pairs-of-parallel-sides-in-shapes-and-choose-the-correct-answer\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_count_parallel_2d_shape_pt.png\" alt=\"Count Pairs of Parallel Sides in Shapes and Choose the Correct Answer Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Pairs of Parallel Sides in Shapes and Choose the Correct Answer Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-definition-of-linear-pair-of-angles-in-geometry\">Definition of Linear Pair of Angles in Geometry<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Two angles are said to form a linear pair if<\/strong><\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>they are adjacent angles<\/strong><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>their non-common arms are opposite rays &amp; form a straight line<\/strong><\/li>\n<\/ol>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/count-sides-and-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/count-sides-and-angles.jpeg\" alt=\"Count Sides and Angles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-pairs-of-equivalent-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/find-pairs-of-equivalent-fractions.jpeg\" alt=\"Find Pairs of Equivalent Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/identify-ordered-pairs-on-coordinate-grid\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/identify-ordered-pairs-on-coordinate-grid.jpeg\" alt=\"Identify Ordered Pairs On Coordinate Grid Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/marking-ordered-pairs-on-coordinate-grid\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/marking-ordered-pairs-on-coordinate-grid.jpeg\" alt=\"Marking Ordered Pairs on Coordinate Grid Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/separate-out-the-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-properties-of-linear-pair-of-angles\">Properties of Linear Pair of Angles<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The angles in a linear pair are supplementary (add up to $180^\\circ$).&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A linear pair of angles are always adjacent angles.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A linear pair of angles always form a straight line.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">They together form a straight angle.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Two angles forming a linear pair have a common vertex and a common arm. Their non-common sides are opposite rays that form a line.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"458\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-of-angles-a-and-b.png\" alt=\"linear pair of angles a and b\" class=\"wp-image-34541\" title=\"linear pair of angles a and b\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-of-angles-a-and-b.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-of-angles-a-and-b-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-linear-pair-postulate\">Linear Pair Postulate<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The linear pair postulate states that if two angles form a linear pair, they are supplementary.&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"326\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/linear-pair-postulate-.png\" alt=\"linear pair postulate\" class=\"wp-image-34543\" title=\"linear pair postulate\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/linear-pair-postulate-.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/linear-pair-postulate--300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The converse of this postulate is not true. It means that if two angles are supplementary, they do not necessarily form a linear pair of angles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Counter example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the image below, angles M and N are supplementary since<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$120^\\circ + 60^\\circ = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">However, they do not form a linear pair of angles. They are not adjacent.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/angles-M-and-N.png\" alt=\"angles M and N\" class=\"wp-image-34544\" title=\"angles M and N\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/angles-M-and-N.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/angles-M-and-N-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-linear-pair-axioms\">Linear Pair Axioms<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s learn two important axioms which are collectively termed as \u2018linear pair axioms\u2019. Axiom is a mathematical statement that is self-evident and accepted to be true.<\/p>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-46af6e0d-d98a-41dd-8f7b-8e6948c43fae\">\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Axiom 1: If a ray stands on a line, then the sum of two adjacent angles formed is <\/strong>$180^\\circ$<strong>.<\/strong><\/p>\n\n\n<\/div>\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The ray OC is standing on a line AB. Thus, the adjacent angles $\\angle AOC$ and $\\angle BOC$ add up to $180^\\circ$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"329\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/angles-AOC-and-BOC-in-a-linear-pair.png\" alt=\"angles AOC and BOC in a linear pair\" class=\"wp-image-34545\" title=\"angles AOC and BOC in a linear pair\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/angles-AOC-and-BOC-in-a-linear-pair.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/angles-AOC-and-BOC-in-a-linear-pair-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The converse of the axiom 1 is also true.<\/p>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-cdd8876a-1ab6-42f1-9ae4-c7e5d5b89d86\">\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Axiom 2:<\/strong> <strong>If two angles form a linear pair, then non-common arms of both the angles form a straight line.<\/strong><\/p>\n\n\n<\/div>\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the diagram shown above, the rays OA and OB are the non-common arms of the angles $\\angle AOC$ and $^\\circ BOC$. Rays OA and OB form a straight line AB.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-linear-pair-perpendicular-theorem\">Linear Pair Perpendicular Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>If two angles forming a linear pair of angles are congruent, then the lines are perpendicular.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"509\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-perpendicular-theorem.png\" alt=\"linear pair perpendicular theorem\" class=\"wp-image-34546\" title=\"linear pair perpendicular theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-perpendicular-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-perpendicular-theorem-300x246.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the angles $\\angle a$ and $\\angle b$ form a linear pair of angles. Also, they are congruent since they measure 90 degrees each.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the lines x and y are perpendicular to each other.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-linear-pair-of-angles-vs-supplementary-angles\">Linear Pair of Angles vs. Supplementary Angles<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is the most common mistake to confuse supplementary angles with linear pairs of angles due to similarity in their properties. However, these are two different terms. Let\u2019s understand the difference.<\/p>\n\n\n\n<figure class=\"wp-block-table wj-custom-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th><strong>Linear Pair of Angles<\/strong><\/th><th><strong>Supplementary Angles<\/strong><\/th><\/tr><\/thead><tbody><tr><td>A linear pair of angles are always adjacent angles. They have a common vertex and a common arm.<\/td><td>Two supplementary angles may or may not be adjacent.<\/td><\/tr><tr><td>These are adjacent angle that add up to $180^\\circ$<\/td><td>These are any two angles that add up to $180^\\circ$<\/td><\/tr><tr><td>All linear pairs of angles are supplementary angles.<\/td><td>Supplementary angles need not form a linear pair of angles.<\/td><\/tr><tr><td><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/image-43.png\" alt=\"\"><\/td><td><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/image-44.png\" alt=\"\"><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-linear-pair-of-angles\">Solved Examples on Linear Pair of Angles<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Observe the diagram and identify the linear pair of angles.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"232\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/lines-AB-and-XY-intersecting-at-point-C.png\" alt=\"lines AB and XY intersecting at point C\" class=\"wp-image-34547\" title=\"lines AB and XY intersecting at point C\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The lines AB and XY intersect at a single point C.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, they form linear pairs of angles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Any two adjacent angles formed here will form a linear pair of angles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Angles in linear pair are:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\\angle ACY$ and $\\angle BCY$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle ACX$ and $\\angle ACY$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle ACX$ and $\\angle BCX$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle BCX$ and $\\angle BCY$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. If two angles forming a linear pair are in the ratio of 7:11, then find the measure of each of the angles.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let the measures of the angles be $(7x)^\\circ$ and $(11x)^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the angles form a linear pair, we can write<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(7x)^\\circ + (11x)^\\circ = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(18x)^\\circ = 180$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Two angles are $7 \\times 10 = 70^\\circ$ and $11 \\times 10 = 110^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Angles <\/strong>$^\\angle ABC$<strong> and <\/strong>$^\\angle DBC$<strong> form a linear pair of angles. Find the measure of <\/strong>$\\angle ABC$<strong> in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"100\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/linear-pair-of-angles-with-one-angle-measuring-48-degree.png\" alt=\"linear pair of angles with one angle measuring 48\u00ba\" class=\"wp-image-34548\" title=\"linear pair of angles with one angle measuring 48\u00ba\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the angles form a linear pair, they are supplementary.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle ABC + m\\angle DBC = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle ABC + 48^\\circ = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle ABC = 180^\\circ \\;-\\; &nbsp;48^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m^\\circ ABC = 132^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. If one angle in the linear pair is <\/strong>$40^\\circ$<strong>, then find the other angle.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Measure of one angle $= 40^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the angles form a linear pair, they add up to $180^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Measure of the other angle $= 180^\\circ \\;\u2013\\; 40^\\circ = 140^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. One angle of the linear pair is thrice the other. Find the angles.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let one angle be $x^\\circ$ and the other angle be<strong> <\/strong>$3x^\\circ$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since they form a linear pair, we write<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x^\\circ + 3x^\\circ = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4x^\\circ = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x^\\circ = 45^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the angles are $45^\\circ$ and $135^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>6. Do angles that measure <\/strong>$107^\\circ$<strong> and <\/strong>$72^\\circ$<strong> form a linear pair?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Angles in a linear pair are supplementary. So, if two angles are not supplementary, they are not a linear pair of angles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$107^\\circ + 72^\\circ = 179^\\circ 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">They do not form a linear pair.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-linear-pair-of-angles\">Practice Problems on Linear Pair of Angles<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Linear Pair of Angles: Definition, Axioms, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following is the linear pair of $75^\\circ$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$95^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$105^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$15^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$125^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $105^\\circ$<br\/>Linear pair of $75^\\circ = 180^\\circ \\;\u2013\\; 75^\\circ = 105^\\circ$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What will be the value of x?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/linear-pair-of-angles-in-terms-of-x.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$72^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$78^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$74^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$79^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $79^\\circ$<br\/>The angles measuring $(2x \\;\u2013\\; 30)$ and $(x \\;\u2013\\; 12)$ form a linear pair.<br>\r\n$2x \\;\u2013\\; 30 + x \\;\u2013\\; 12 = 180^\\circ$<br>\r\n$3x \\;\u2013\\; 42 = 180^\\circ$<br>\r\n$3x = 222^\\circ$<br>\r\n$x = 74^\\circ$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following pairs of angles form a linear pair?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$123^\\circ$ and $57^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$145^\\circ$ and $25^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$125^\\circ$ and $45^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$109^\\circ$ and $70^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $123^\\circ$ and $57^\\circ$<br\/>$123^\\circ + 57^\\circ = 180^\\circ$. They form a linear pair.<br>\r\n$145^\\circ + 25^\\circ = 170^\\circ$. They do not form a linear pair.<br>\r\n$125^\\circ + 45^\\circ = 170^\\circ$. They do not form a linear pair.<br>\r\n$109^\\circ + 70^\\circ = 179^\\circ$. They do not form a linear pair.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following pairs of angles form a linear pair?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/identifying-linear-pair-of-angles.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\angle1$ and $\\angle4$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\angle2$ and $\\angle3$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\angle1$ and $\\angle5$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\angle3$ and $\\angle5$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\angle1$ and $\\angle5$<br\/>$\\angle1$ and $\\angle4$ are not adjacent angles.<br>\r\n$\\angle2$ and $\\angle3$ are adjacent angles but are not supplementary.<br>\r\n$\\angle3$ and $\\angle5$ are not adjacent.<br>\r\n$\\angle1$ and $\\angle5$ are adjacent angles and are supplementary. Thus, they form a linear pair.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What will be the value of k in the following figure?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/angles-measuring-7k-and-2k-forming-a-linear-pair.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">10<\/div><div class=\"spq_answer_block\" data-value=\"1\">20<\/div><div class=\"spq_answer_block\" data-value=\"2\">30<\/div><div class=\"spq_answer_block\" data-value=\"3\">40<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 20<br\/>$\\angle POQ$ and $\\angle POR$ form a linear pair of angles.<br>\r\n$\\angle POQ + \\angle POR = 180^\\circ$<br>\r\n$(7k)^\\circ + (2k)^\\circ = 180^\\circ$<br>\r\n$(9k)^\\circ = 180^\\circ$<br>\r\n$k = 20$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Linear Pair of Angles: Definition, Axioms, Examples, Facts, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Linear Pair of Angles\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the linear pair of $$75^\\\\circ$$?\",\n                    \"text\": \"Which of the following is the linear pair of $$75^\\\\circ$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Linear pair of $$75^\\\\circ = 180^\\\\circ \\\\;\u2013\\\\; 75^\\\\circ = 105^\\\\circ$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$95^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Linear pair of $$75^\\\\circ = 180^\\\\circ \\\\;\u2013\\\\; 75^\\\\circ = 105^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$15^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Linear pair of $$75^\\\\circ = 180^\\\\circ \\\\;\u2013\\\\; 75^\\\\circ = 105^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$125^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Linear pair of $$75^\\\\circ = 180^\\\\circ \\\\;\u2013\\\\; 75^\\\\circ = 105^\\\\circ$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$105^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Linear pair of $$75^\\\\circ = 180^\\\\circ \\\\;\u2013\\\\; 75^\\\\circ = 105^\\\\circ$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Linear pair of $$75^\\\\circ = 180^\\\\circ \\\\;\u2013\\\\; 75^\\\\circ = 105^\\\\circ$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What will be the value of x?\",\n                    \"text\": \"What will be the value of x? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/linear-pair-of-angles-in-terms-of-x.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The angles measuring $$(2x \\\\;\u2013\\\\; 30)$$ and $$(x \\\\;\u2013\\\\; 12)$$ form a linear pair.<br>\r\n$$2x \\\\;\u2013\\\\; 30 + x \\\\;\u2013\\\\; 12 = 180^\\\\circ$$<br>\r\n$$3x \\\\;\u2013\\\\; 42 = 180^\\\\circ$$<br>\r\n$$3x = 222^\\\\circ$$<br>\r\n$$x = 74^\\\\circ$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$72^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angles measuring $$(2x \\\\;\u2013\\\\; 30)$$ and $$(x \\\\;\u2013\\\\; 12)$$ form a linear pair.<br>\r\n$$2x \\\\;\u2013\\\\; 30 + x \\\\;\u2013\\\\; 12 = 180^\\\\circ$$<br>\r\n$$3x \\\\;\u2013\\\\; 42 = 180^\\\\circ$$<br>\r\n$$3x = 222^\\\\circ$$<br>\r\n$$x = 74^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$78^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angles measuring $$(2x \\\\;\u2013\\\\; 30)$$ and $$(x \\\\;\u2013\\\\; 12)$$ form a linear pair.<br>\r\n$$2x \\\\;\u2013\\\\; 30 + x \\\\;\u2013\\\\; 12 = 180^\\\\circ$$<br>\r\n$$3x \\\\;\u2013\\\\; 42 = 180^\\\\circ$$<br>\r\n$$3x = 222^\\\\circ$$<br>\r\n$$x = 74^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$74^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The angles measuring $$(2x \\\\;\u2013\\\\; 30)$$ and $$(x \\\\;\u2013\\\\; 12)$$ form a linear pair.<br>\r\n$$2x \\\\;\u2013\\\\; 30 + x \\\\;\u2013\\\\; 12 = 180^\\\\circ$$<br>\r\n$$3x \\\\;\u2013\\\\; 42 = 180^\\\\circ$$<br>\r\n$$3x = 222^\\\\circ$$<br>\r\n$$x = 74^\\\\circ$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$79^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The angles measuring $$(2x \\\\;\u2013\\\\; 30)$$ and $$(x \\\\;\u2013\\\\; 12)$$ form a linear pair.<br>\r\n$$2x \\\\;\u2013\\\\; 30 + x \\\\;\u2013\\\\; 12 = 180^\\\\circ$$<br>\r\n$$3x \\\\;\u2013\\\\; 42 = 180^\\\\circ$$<br>\r\n$$3x = 222^\\\\circ$$<br>\r\n$$x = 74^\\\\circ$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The angles measuring $$(2x \\\\;\u2013\\\\; 30)$$ and $$(x \\\\;\u2013\\\\; 12)$$ form a linear pair.<br>\r\n$$2x \\\\;\u2013\\\\; 30 + x \\\\;\u2013\\\\; 12 = 180^\\\\circ$$<br>\r\n$$3x \\\\;\u2013\\\\; 42 = 180^\\\\circ$$<br>\r\n$$3x = 222^\\\\circ$$<br>\r\n$$x = 74^\\\\circ$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following pairs of angles form a linear pair?\",\n                    \"text\": \"Which of the following pairs of angles form a linear pair?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$123^\\\\circ + 57^\\\\circ = 180^\\\\circ$$. They form a linear pair.<br>\r\n$$145^\\\\circ + 25^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$125^\\\\circ + 45^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$109^\\\\circ + 70^\\\\circ = 179^\\\\circ$$. They do not form a linear pair.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$145^\\\\circ$$ and $$25^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$123^\\\\circ + 57^\\\\circ = 180^\\\\circ$$. They form a linear pair.<br>\r\n$$145^\\\\circ + 25^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$125^\\\\circ + 45^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$109^\\\\circ + 70^\\\\circ = 179^\\\\circ$$. They do not form a linear pair.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$125^\\\\circ$$ and $$45^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$123^\\\\circ + 57^\\\\circ = 180^\\\\circ$$. They form a linear pair.<br>\r\n$$145^\\\\circ + 25^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$125^\\\\circ + 45^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$109^\\\\circ + 70^\\\\circ = 179^\\\\circ$$. They do not form a linear pair.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$109^\\\\circ$$ and $$70^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$123^\\\\circ + 57^\\\\circ = 180^\\\\circ$$. They form a linear pair.<br>\r\n$$145^\\\\circ + 25^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$125^\\\\circ + 45^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$109^\\\\circ + 70^\\\\circ = 179^\\\\circ$$. They do not form a linear pair.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$123^\\\\circ$$ and $$57^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$123^\\\\circ + 57^\\\\circ = 180^\\\\circ$$. They form a linear pair.<br>\r\n$$145^\\\\circ + 25^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$125^\\\\circ + 45^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$109^\\\\circ + 70^\\\\circ = 179^\\\\circ$$. They do not form a linear pair.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$123^\\\\circ + 57^\\\\circ = 180^\\\\circ$$. They form a linear pair.<br>\r\n$$145^\\\\circ + 25^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$125^\\\\circ + 45^\\\\circ = 170^\\\\circ$$. They do not form a linear pair.<br>\r\n$$109^\\\\circ + 70^\\\\circ = 179^\\\\circ$$. They do not form a linear pair.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following pairs of angles form a linear pair?\",\n                    \"text\": \"Which of the following pairs of angles form a linear pair? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/identifying-linear-pair-of-angles.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\angle1$$ and $$\\\\angle4$$ are not adjacent angles.<br>\r\n$$\\\\angle2$$ and $$\\\\angle3$$ are adjacent angles but are not supplementary.<br>\r\n$$\\\\angle3$$ and $$\\\\angle5$$ are not adjacent.<br>\r\n$$\\\\angle1$$ and $$\\\\angle5$$ are adjacent angles and are supplementary. Thus, they form a linear pair.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle1$$ and $$\\\\angle4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle1$$ and $$\\\\angle4$$ are not adjacent angles.<br>\r\n$$\\\\angle2$$ and $$\\\\angle3$$ are adjacent angles but are not supplementary.<br>\r\n$$\\\\angle3$$ and $$\\\\angle5$$ are not adjacent.<br>\r\n$$\\\\angle1$$ and $$\\\\angle5$$ are adjacent angles and are supplementary. Thus, they form a linear pair.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle2$$ and $$\\\\angle3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle1$$ and $$\\\\angle4$$ are not adjacent angles.<br>\r\n$$\\\\angle2$$ and $$\\\\angle3$$ are adjacent angles but are not supplementary.<br>\r\n$$\\\\angle3$$ and $$\\\\angle5$$ are not adjacent.<br>\r\n$$\\\\angle1$$ and $$\\\\angle5$$ are adjacent angles and are supplementary. Thus, they form a linear pair.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle3$$ and $$\\\\angle5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle1$$ and $$\\\\angle4$$ are not adjacent angles.<br>\r\n$$\\\\angle2$$ and $$\\\\angle3$$ are adjacent angles but are not supplementary.<br>\r\n$$\\\\angle3$$ and $$\\\\angle5$$ are not adjacent.<br>\r\n$$\\\\angle1$$ and $$\\\\angle5$$ are adjacent angles and are supplementary. Thus, they form a linear pair.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\angle1$$ and $$\\\\angle5$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\angle1$$ and $$\\\\angle4$$ are not adjacent angles.<br>\r\n$$\\\\angle2$$ and $$\\\\angle3$$ are adjacent angles but are not supplementary.<br>\r\n$$\\\\angle3$$ and $$\\\\angle5$$ are not adjacent.<br>\r\n$$\\\\angle1$$ and $$\\\\angle5$$ are adjacent angles and are supplementary. Thus, they form a linear pair.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\angle1$$ and $$\\\\angle4$$ are not adjacent angles.<br>\r\n$$\\\\angle2$$ and $$\\\\angle3$$ are adjacent angles but are not supplementary.<br>\r\n$$\\\\angle3$$ and $$\\\\angle5$$ are not adjacent.<br>\r\n$$\\\\angle1$$ and $$\\\\angle5$$ are adjacent angles and are supplementary. Thus, they form a linear pair.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What will be the value of k in the following figure?\",\n                    \"text\": \"What will be the value of k in the following figure? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/05\/angles-measuring-7k-and-2k-forming-a-linear-pair.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\angle POQ$$ and $$\\\\angle POR$$ form a linear pair of angles.<br>\r\n$$\\\\angle POQ + \\\\angle POR = 180^\\\\circ$$<br>\r\n$$(7k)^\\\\circ + (2k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$(9k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$k = 20$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle POQ$$ and $$\\\\angle POR$$ form a linear pair of angles.<br>\r\n$$\\\\angle POQ + \\\\angle POR = 180^\\\\circ$$<br>\r\n$$(7k)^\\\\circ + (2k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$(9k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$k = 20$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle POQ$$ and $$\\\\angle POR$$ form a linear pair of angles.<br>\r\n$$\\\\angle POQ + \\\\angle POR = 180^\\\\circ$$<br>\r\n$$(7k)^\\\\circ + (2k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$(9k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$k = 20$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"40\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle POQ$$ and $$\\\\angle POR$$ form a linear pair of angles.<br>\r\n$$\\\\angle POQ + \\\\angle POR = 180^\\\\circ$$<br>\r\n$$(7k)^\\\\circ + (2k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$(9k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$k = 20$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"20\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\angle POQ$$ and $$\\\\angle POR$$ form a linear pair of angles.<br>\r\n$$\\\\angle POQ + \\\\angle POR = 180^\\\\circ$$<br>\r\n$$(7k)^\\\\circ + (2k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$(9k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$k = 20$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\angle POQ$$ and $$\\\\angle POR$$ form a linear pair of angles.<br>\r\n$$\\\\angle POQ + \\\\angle POR = 180^\\\\circ$$<br>\r\n$$(7k)^\\\\circ + (2k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$(9k)^\\\\circ = 180^\\\\circ$$<br>\r\n$$k = 20$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-linear-pair-of-angles\">Frequently Asked Questions on Linear Pair of Angles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\"><strong>How many angles are there in a linear pair?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Only two angles can be found in a linear pair.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\"><strong>Are linear pairs of angles congruent?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Linear pairs of angles are not congruent. When the measure of each of the angles in a linear pair is $90^\\circ$, a linear pair of angles are congruent.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\"><strong>Are the linear pair of angles always supplementary?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Supplementary is one of the necessary conditions for angles to be a linear pair. Hence, linear pairs are always supplementary. A linear pair forms a straight angle that measures $180^\\circ$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\"><strong>What is the difference between a linear pair of angles and complementary angles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A linear pair are two adjacent angles that sum to $180^\\circ$. On the other hand, complementary angles are the angles that sum up to $90^\\circ$. Complementary angles need not be adjacent.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\"><strong>What is the difference between a linear pair of angles and vertical angles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-4ee08e46-3dd5-4950-b8c8-7b6fd4a4761b\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A linear pair are two adjacent angles that sum to $180^\\circ$. They share a common vertex and a common arm.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Vertical angles are the angles that are opposite angles formed when two lines intersect each other. They only share a common vertex. Vertical angles are always congruent.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Linear Pair Of Angles? A linear pair of angles is a pair of adjacent angles formed when two lines intersect each other at a single point.&nbsp; \u201cLinear\u201d simply means \u201carranged along a straight line.\u201d We know that a straight angle is an angle that measures $180^\\circ$. It is called a straight angle &#8230; <a title=\"Linear Pair of Angles: Definition, Axioms, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/linear-pair-of-angles\" aria-label=\"More on Linear Pair of Angles: Definition, Axioms, Examples, Facts, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-28473","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28473","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=28473"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28473\/revisions"}],"predecessor-version":[{"id":37401,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28473\/revisions\/37401"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=28473"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=28473"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=28473"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}