Question

(a) an angle measures 37°. what is the measure of its complement? (b) an angle measures 61°. what is the measure of its supplement? measure of the complement: ° measure of the supplement: °

Explanation:

Step1: Recall complement formula

Complementary angles add up to 90°. Let the given angle be $\theta = 37^{\circ}$. The measure of the complement $\alpha$ is $\alpha=90^{\circ}-\theta$.

Step2: Calculate complement

$\alpha = 90^{\circ}-37^{\circ}=53^{\circ}$.

Step3: Recall supplement formula

Supplementary angles add up to 180°. Let the given angle be $\beta = 61^{\circ}$. The measure of the supplement $\gamma$ is $\gamma = 180^{\circ}-\beta$.

Step4: Calculate supplement

$\gamma=180^{\circ}-61^{\circ}=119^{\circ}$.

Answer:

measure of the complement: $53^{\circ}$
measure of the supplement: $119^{\circ}$