(a) An angle measures \( 27^{\circ} \). What is the measure of its complement? (b) An angle measures \( 120^{\circ} \). What is the measure of its supplement? measure of the complement:

To solve the problems, we need to understand the concepts of complementary and supplementary angles. 1. **Complementary Angles**: Two angles are complementary if the sum of their measures is \(90^{\circ}\). Therefore, the measure of the complement of an angle \(a\) can be calculated as: \[ \text{Complement} = 90^{\circ} - a \] 2. **Supplementary Angles**: Two angles are supplementary if the sum of their measures is \(180^{\circ}\). Therefore, the measure of the supplement of an angle \(b\) can be calculated as: \[ \text{Supplement} = 180^{\circ} - b \] Now, let's solve each part step by step. ### Part (a) Given an angle measures \(27^{\circ}\): \[ \text{Complement} = 90^{\circ} - 27^{\circ} \] Calculating this: \[ \text{Complement} = 90 - 27 = 63^{\circ} \] ### Part (b) Given an angle measures \(120^{\circ}\): \[ \text{Supplement} = 180^{\circ} - 120^{\circ} \] Calculating this: \[ \text{Supplement} = 180 - 120 = 60^{\circ} \] ### Final Answers - The measure of the complement of \(27^{\circ}\) is \(63^{\circ}\). - The measure of the supplement of \(120^{\circ}\) is \(60^{\circ}\).