Question

(a) an angle measures 110°. what is the measure of its supplement? (b) an angle measures 59°. 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 $\theta = 110^{\circ}$, and the supplement be $x$. Then $\theta+x = 180^{\circ}$.

Step2: Solve for the supplement

$x=180^{\circ}-\theta = 180^{\circ}- 110^{\circ}=70^{\circ}$

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the given angle be $\alpha = 59^{\circ}$, and the complement be $y$. Then $\alpha + y=90^{\circ}$.

Step4: Solve for the complement

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

Answer:

measure of the supplement: $70^{\circ}$
measure of the complement: $31^{\circ}$