Fundamental Concepts
22. Supplementary Angles · add up to 180°
The two adjacent angles on a straight line always add up to 180°.
Two angles are supplementary when their sum is exactly 180° — together they make a straight line. When two supplementary angles sit side by side on a straight line like this, the pair is called a linear pair. Drag C — ∠AOC and ∠COB always add up to 180° because they sit along the straight line AB.
What this lesson covers
Try to break it
Let's pull them apart! Drag C all the way to the left or right. Watch how one angle grows while the other shrinks. They're like a seesaw — when one goes up, the other goes down, but their total stays locked at 180°.
How you build it
Make a linear pair of supplementary angles.
- Place point A on the left.
- Place point B on the right.
- Draw line AB.
- Place point O between A and B on the line.
- Place point C above line AB.
- Draw ray OC. ∠AOC + ∠COB = 180° — supplementary.
The proof, step by step
Prove that ∠AOC and ∠BOC are supplementary.
- Points A, O and B lie on one straight line.
- A straight line forms a straight angle of exactly 180°.
- Ray OC divides that straight angle into two adjacent angles, ∠AOC and ∠BOC.
- Together the two angles fill the straight angle, so ∠AOC + ∠BOC = 180°.
- Two angles whose measures add up to 180° are supplementary — so ∠AOC and ∠BOC are supplementary.
Worked example
Two angles are supplementary. If one angle measures 65°, what is the measure of the other angle?
Supplementary angles add up to 180°. If one angle is 65°, the other is 180° - 65° = 115°.
- 115° — correct
- 125°
- 25°
- 35°