45-Degree Angle – Definition with Examples

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Angle Definition

​​When two rays intersect at a common endpoint, they form an angle. The common endpoint is called the vertex, and the rays are called the arms of the angle.

arms of the angle. - SplashLearn

An angle is measured in° or radians. If the two arms of an angle extend in exactly opposite directions, it is a straight angle. A straight angle measures 180°. An angle can be measured using a protractor, and the angle of measure at 90 degrees is called a right angle. At a right angle, the two arms are perpendicular to each other. 

right angle - SplashLearn

What is a 45-Degree Angle?

When the right angle is divided into two equal parts each angle measures 45°.

two equal parts of right angle - SplashLearn

A 45-degree angle is an acute angle. It is half of the right angle or a 90-degree angle. Take a look at the image of the 45-degree angle.

45-degree angle - SplashLearn

Real-Life Examples of 45-degree Angle

We can see the 45-degree angle in a variety of places around us. For example, if the laptop screen is bent properly, it will form a 45-degree angle with the keyboard.
Similarly, if a door is opened halfway, it will form a 45-degree angle with the wall. 

Consider the following examples of 45-degree angles found in our environment:

  • A 45-degree angle allows the sun’s rays to travel the greatest distance. That is why some solar panels are angled at 45 degrees, depending on their geographical location.
  • When throwing a ball, the 45-degree angle is optimal because it reaches the farthest. 
  • In architecture, the 45-degree angle is used to create designer doors and window grills.

Fun Facts About the 45-degree Angle

  • A square’s diagonals form a 45-degree angle with its sides.
  • An isosceles right triangle will have one right angle and two 45 degrees angles.

Construction of 45° Angle:

  • a) Using a Protractor 

The steps in forming a 45-degree angle are as follows:

Step 1: Draw a ray and name it AB.

Construction of 45° Angle : Draw a Line - SplashLearn

Step 2: Keep the center point of the protractor at A. Since the angle opens to the right, choose 45° in the list that starts at the right and moves in the anticlockwise direction. Mark the point C.

Construction of 45° Angle : use protracttor - SplashLearn

Step 3: Join A and C. Here are the measures.

a) Using a Compass

The steps in forming a 45-degree angle are as follows:

Step 1: Mark point A to create a 45° angle.

Construction of 45° Angle : Using a Compass - SplashLearn

Step 2: Create a 90° angle first. Extend your compass beyond half the length of AB. Mark an arc above and below line segment AB with the sharp end.

Construction of 45° Angle : Create a 90° angle first - SplashLearn

Step 3: Keeping the compass at its original width, place the sharp end at B and draw arcs above and below line segment AB to intersect with the arcs drawn in step 2.

Keeping the compass at its original width - SplashLearn

Step 4: Draw a straight line connecting the two points where the arcs intersect. This line bisects AB perpendicularly. P is AB’s midpoint.

Perpendicular Bisector - SplashLearn

Step 5: Bisect the 90-degree angle in half to create a 45-degree angle.

Bisect the 90-degree angle in half to create a 45-degree angle. - SplashLearn

In summary, the steps involved in constructing a 45° angle are as follows:

  1. Create perpendicular lines to make a 90° angle.
  2. Divide the 90° angle in half to obtain a 45° angle.

Solved Examples

Example 1: What is the measurement of one-fourth of a 180° angle?

Solution:

One-fourth of 180° angle = 180/4 = 45

One-fourth of a 180° angle is a 45° angle.

Example 2: Tim drew a horizontal line on a piece of paper. By drawing a vertical line, Ron divided it in half. Upon his arrival, Jack further divided the two halves into four equal halves.  

How many 45-degree angles are drawn on the paper?

Solution:

By drawing a vertical line on a horizontal line, Tim made two 90° angles. 

Splitting each 90° angle in half yields two 45° angles. 

So in all, there are four 45° angles..

four 45° angles - SplashLearn

Practice Problems

45 Degree Angle

Attend this Quiz & Test your knowledge.

1A 45-degree angle is an example of what type of angle?

Acute Angle
Right Angle
Straight Angle
Obtuse Angle
CorrectIncorrect
Correct answer is: Acute Angle
Angles smaller than 90-degree are acute angles.

2Which of the following measures is not a right angle?

(2 x 45) degree
90 degree
(2 x 90) degree
(3 x 30) degree
CorrectIncorrect
Correct answer is: (2 x 90) degree
(2 X 90) degree gives 180 degrees, which forms a straight line.

3An obtuse angle is _____ than a right angle.

Smaller
Greater
Equal To
None of the above
CorrectIncorrect
Correct answer is: Greater
Angles greater than 90 degrees are obtuse angles.

4Two right angles make a _____ angle.

Reflex angle
Straight angle
Complete angle
Right angle
CorrectIncorrect
Correct answer is: Straight angle
Two right angles make a 180-degree angle which gives a straight line.

5The time on an analog clock when the hour and minute hand make an angle that is more than a right angle is

3 pm
11 pm
5 pm
2 pm
CorrectIncorrect
Correct answer is: 5 pm
The time on an analog clock when the hour and minute hand make an angle that is more than a right angle among the given options is 5 pm.

Conclusion
We hope that with this lesson, we have tried to cover some basic definitions, the geometry of the 45-degree Angle, and real-life examples, which should give you at least a basic idea of what a 45-degree angle is. With the help of SplashLearn, you can learn how to learn better. You can download the SplashLearn App today, which will help you clear your doubts. Once you install the app, you can clear all your doubts on 45-degree Angle, trigonometry, and more such topics on your phone.

Frequently Asked Questions

45-degree angle is an acute angle measuring 45 degrees.

When an angle bisector is drawn for a 90-degree angle, the resulting smaller angles are 45 degrees each.

You can draw two perpendicular lines on a piece of paper. Then, divide the resulting right angle into two equal parts. Each equal part gives a 45-degree angle.

Place your protractor along any vertex of the rectangle and mark a point at 45 degrees. Now, remove the protractor and join the vertex with the point with a ruler.

A 45-degree angle allows the sun’s rays to travel the greatest distance. That is why some solar panels are angled at 45 degrees, depending on their geographical location.

When throwing a ball, the 45-degree angle is optimal because it reaches the farthest.


45-Degree Angle – Definition with Examples

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45-Degree Angle – Definition with Examples

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45-Degree Angle – Definition with Examples

Parallel and Perpendicular Lines

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