Lines and Angles
89. The 90° and 180° Pairs · Complementary and supplementary angles
The two angles on a straight line always add to 180°, and the two angles in a right angle always add to 90°.
Two angles are complementary when their sum is 90° (a right angle). Two angles are supplementary when their sum is 180° (a straight line). Angles forming a straight line are always supplementary.
What this lesson covers
Try to break it
Try dragging the ray all around the circle. No matter where you put it, the two angles always sum to 180° for the straight line and 90° for the right angle. It never breaks — that's the theorem!
How you build it
Build a linear pair and measure the two angles.
- Draw a straight line.
- Place a point on the line.
- Draw a ray from the point.
- Drag the gold protractor so its centre sits on vertex A, then turn it to measure the two angles on the line.
The proof, step by step
Prove that the two angles formed when a ray stands on a straight line are supplementary.
- A straight angle measures 180°.
- When a ray stands on a line, it forms two adjacent angles.
- The sum of these two angles is equal to the straight angle, 180°.
- Therefore, the angles are supplementary.
Worked example
Two angles are supplementary. If one angle is 110°, what is the measure of the other angle?
Supplementary angles add up to 180°. So, 180° - 110° = 70°.
- 70° — correct
- 110°
- 90°
- 55°