Complementary and Supplementary Angles

Complementary angles add up to 90°. Supplementary angles add up to 180°. This lesson shows how to spot each pair in a diagram and use the sum to find a missing angle.

Two angles can have special relationships based on their sum:

• Complementary angles: Two angles whose measures add up to 90°. If ∠A + ∠B = 90°, then ∠A and ∠B are complementary. Example: 30° and 60° are complementary.

• Supplementary angles: Two angles whose measures add up to 180°. If ∠A + ∠B = 180°, then ∠A and ∠B are supplementary. Example: 110° and 70° are supplementary (they form a straight line).

Important notes:

• Complementary and supplementary angles do not need to be adjacent (next to each other), though they often are.
• If they are adjacent and supplementary, they form a straight line.
• If they are adjacent and complementary, they form a right angle.

1. Two angles are complementary. One measures 35°. What is the other?

   $90° - 35° = 55°$

2. Two angles are supplementary. One measures 120°. What is the other?

   $180° - 120° = 60°$

3. ∠A and ∠B are adjacent and form a right angle. If ∠A = 28°, what is ∠B?

   They are complementary → ∠B = 90° − 28° = 62°.

Complementary and supplementary angles appear in many practical situations:

• Construction: Walls meeting at a corner usually form a 90° (right) angle. The two angles on either side are complementary if they make up that corner.
• Design: When laying tiles or flooring, angles that add to 180° (supplementary) help create straight edges.
• Navigation: Turning angles on a map or GPS often involve supplementary relationships (turning left then right to go straight).
• Everyday objects: The angles formed by the back and seat of a chair, or the hands of a clock at certain times.

Recognizing these relationships helps you calculate missing angles without measuring everything directly.