Question

(a) an angle measures 32°. what is the measure of its complement? (b) an angle measures 31°. 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 $\theta = 32^{\circ}$. The measure of its complement $x$ is $x=90^{\circ}-\theta$.

Step2: Calculate complement

$x = 90^{\circ}-32^{\circ}=58^{\circ}$.

Step3: Recall supplement formula

Supplementary angles add up to 180°. Let the given angle be $\alpha = 31^{\circ}$. The measure of its supplement $y$ is $y = 180^{\circ}-\alpha$.

Step4: Calculate supplement

$y=180^{\circ}-31^{\circ}=149^{\circ}$.

Answer:

measure of the complement: $58^{\circ}$
measure of the supplement: $149^{\circ}$