To solve this problem, we need to understand two concepts:

1. Complementary Angles: Two angles are complementary if their measures add up to 90°.
2. Supplementary Angles: Two angles are supplementary if their measures add up to 180°.

Given this information, let's solve each part.

(a) Finding the Complement of 52°

To find the complement of 52°, subtract it from 90°: $90^\circ - 52^\circ = 38^\circ$

So, the measure of the complement of 52° is 38°.

(b) Finding the Supplement of 119°

To find the supplement of 119°, subtract it from 180°: $180^\circ - 119^\circ = 61^\circ$

Thus, the measure of the supplement of 119° is 61°.

Answers

• Measure of the complement (a): 38°
• Measure of the supplement (b): 61°

Would you like further explanation on complementary and supplementary angles, or do you have any questions?

Here are 5 additional questions to expand your understanding:

1. What is the complement of a 45° angle?
2. What is the supplement of a 72° angle?
3. If an angle is 80°, what would its complement and supplement be?
4. How are complementary and supplementary angles used in real-life geometry problems?
5. Can an angle have both a complement and a supplement? Why or why not?

Tip: Remember, complementary angles always sum to 90°, and supplementary angles always sum to 180°.