Question

(a) an angle measures 59°. what is the measure of its complement? (b) an angle measures 132°. what is the measure of its supplement? measure of the complement: measure of the supplement:

Explanation:

Step1: Recall complement - angle formula

Complementary angles add up to 90°. Let the given angle be $\theta_1 = 59^{\circ}$. The measure of its complement $\alpha$ is given by $\alpha=90^{\circ}-\theta_1$.

Step2: Calculate the complement

$\alpha = 90^{\circ}-59^{\circ}=31^{\circ}$.

Step3: Recall supplement - angle formula

Supplementary angles add up to 180°. Let the given angle be $\theta_2 = 132^{\circ}$. The measure of its supplement $\beta$ is given by $\beta = 180^{\circ}-\theta_2$.

Step4: Calculate the supplement

$\beta=180^{\circ}-132^{\circ}=48^{\circ}$.

Answer:

measure of the complement: $31^{\circ}$
measure of the supplement: $48^{\circ}$