Question

(a) an angle measures 82°. what is the measure of its supplement? (b) an angle measures 31°. what is the measure of its complement? measure of the supplement: ° measure of the complement: °

Explanation:

Step1: Recall supplement - angle formula

The sum of an angle and its supplement is 180°. Let the given angle be $\theta = 82^{\circ}$. The measure of its supplement $\alpha$ is given by $\alpha=180^{\circ}-\theta$.

Step2: Calculate the supplement

$\alpha = 180^{\circ}-82^{\circ}=98^{\circ}$

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the given angle be $\beta = 31^{\circ}$. The measure of its complement $\gamma$ is given by $\gamma = 90^{\circ}-\beta$.

Step4: Calculate the complement

$\gamma=90^{\circ}-31^{\circ}=59^{\circ}$

Answer:

measure of the supplement: 98°
measure of the complement: 59°