Question

(a) an angle measures 91°. what is the measure of its supplement? (b) an angle measures 37°. 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 $\theta = 91^{\circ}$, and its supplement be $x$. Then $x=180^{\circ}-\theta$.

Step2: Calculate the supplement

Substitute $\theta = 91^{\circ}$ into the formula: $x = 180 - 91=89^{\circ}$.

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the given angle be $\alpha = 37^{\circ}$, and its complement be $y$. Then $y = 90^{\circ}-\alpha$.

Step4: Calculate the complement

Substitute $\alpha = 37^{\circ}$ into the formula: $y=90 - 37 = 53^{\circ}$.

Answer:

measure of the supplement: $89^{\circ}$
measure of the complement: $53^{\circ}$