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.
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 90 degrees is called a right angle. In a right angle, the two arms are perpendicular to each other.
When the right angle is divided into two equal parts each angle measures 45°.
Constructing a angle using a protractor
Step 1: Draw a ray and name it AB.
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.
Step 3: Join A and C. Here, measures .
45 Degree Angles in Real Life:
Symmetric windows
Based on the location and climate of the place, some solar panels are installed at an angle of 45° for optimal solar energy production
Additional Knowledge:
Constructing a angle using a compass
Step 1: Draw a line segment and the perpendicular bisector of by intersecting the arcs of radius more than half of the length MN. Let the perpendicular bisector intersect the line segment at O.
Step 2: Draw an arc centered at O with a radius OM, cutting the perpendicular bisector at P.
Step 3: Join M and P using a straight line. measures .
An angle of measure degree can also be constructed by constructing the angular bisector of a right angle.
Fun Facts
