(a) An angle measures $$ 31^{\circ} $$. What is the measure of its complement? (b) An angle measures $$ 72^{\circ} $$. What is the measure of its supplement? measure of the complement:

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UpStudy AI · Accepted Answer

To solve the problems, we need to understand the definitions of complementary and supplementary angles:

1. **Complementary Angles**: Two angles are complementary if the sum of their measures is $$ 90^{\circ} $$. Therefore, the complement of an angle $$ a $$ can be found using the formula:
   $$
   \text{Complement} = 90^{\circ} - a
   $$

2. **Supplementary Angles**: Two angles are supplementary if the sum of their measures is $$ 180^{\circ} $$. Therefore, the supplement of an angle $$ b $$ can be found using the formula:
   $$
   \text{Supplement} = 180^{\circ} - b
   $$

Now, let's solve each part step by step.

### Part (a)
Given an angle measuring $$ 31^{\circ} $$:
- To find the complement:
$$
\text{Complement} = 90^{\circ} - 31^{\circ}
$$

Calculating this:
$$
\text{Complement} = 90 - 31 = 59^{\circ}
$$

### Part (b)
Given an angle measuring $$ 72^{\circ} $$:
- To find the supplement:
$$
\text{Supplement} = 180^{\circ} - 72^{\circ}
$$

Calculating this:
$$
\text{Supplement} = 180 - 72 = 108^{\circ}
$$

### Final Answers
- The measure of the complement of $$ 31^{\circ} $$ is $$ 59^{\circ} $$.
- The measure of the supplement of $$ 72^{\circ} $$ is $$ 108^{\circ} $$.
- The complement of $$ 31^{\circ} $$ is $$ 59^{\circ} $$. - The supplement of $$ 72^{\circ} $$ is $$ 108^{\circ} $$.

(a) An angle measures \( 31^{\circ} \). What is the measure of its complement? (b) An angle measures \( 72^{\circ} \). What is the measure of its supplement? measure of the complement:

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