Supplementary angles are two angles that add up to give a straight angle, 180°

Example of Supplementary Angles

In the example shown, 125° and 55° add up to give 180°, so they are called supplementary angles.

Video Examples:Supplementary Angles

Solved Example on Supplementary Angles

Ques: ∠A and ∠B are supplementary angles and ∠A = ∠B. What are the measures of ∠A and ∠B?

Choices:

A. 60°,120°
B. 180°, 180°
C. 45°, 45°
D. 90°, 90°
Correct Answer: D

Solution:

Step 1: Supplementary angles are two angles that add up to give a straight angle, 180°
Step 2: Given ∠A and ∠B are supplementary angles and m∠A = m∠B.
Step 3: Let m∠A = m∠B = x, then m∠A + m∠B = 180°
Step 4: x + x = 180° [Substitute ∠A = ∠B = x in step 2.]
Step 5: 2x = 180°
Step 6: [Divide by 2.]
Step 7: So, m∠A = m∠B = 90°