Fundamental Concepts
13. Supplementary Angles · adjacent angles always add up to 180°
∠AOC and ∠COB always sum to 180° as C moves anywhere.
Supplementary angles are two angles that add up to 180° (degrees).
What this lesson covers
Try to break it
What happens if you drag C all the way down? Do the angles still add up to a straight line?
How you build it
Make adjacent angles on a straight line.
- Place point A on the left.
- Place point B to the right of A on the same horizontal level.
- Draw line AB (Line tool: A then B). This is the straight line.
- Place point O somewhere between A and B on the line.
- Place point C above the line AB.
- Draw ray OC (Ray tool: O then C). Now ∠AOC and ∠COB sit side-by-side on a straight line — they must add to 180°.
The proof, step by step
Prove that ∠AOC + ∠COB = 180°.
- Points A, O, B lie on a straight line.
- A straight angle measures exactly 180°.
- Ray OC divides the straight angle into ∠AOC and ∠COB.
- Therefore, ∠AOC + ∠COB = 180°.
Worked example
Two straight lines intersect at point O. If one of the adjacent angles formed is 110°, find the measure of the other adjacent angle.
Adjacent angles on a straight line sum to 180°. Subtract the given angle from 180°: 180° - 110° = 70°.
- 60°
- 70° — correct
- 80°
- 90°