Question

(a) an angle measures 71°. what is the measure of its supplement? (b) an angle measures 62°. what is the measure of its complement?

Explanation:

Step1: Recall supplement - angle formula

Two angles are supplementary if their sum is 180°. Let the given angle be $\theta_1 = 71^{\circ}$, and its supplement be $x$. Then $x+\theta_1=180^{\circ}$.

Step2: Solve for the supplement

$x = 180^{\circ}-71^{\circ}=109^{\circ}$.

Step3: Recall complement - angle formula

Two angles are complementary if their sum is 90°. Let the given angle be $\theta_2 = 62^{\circ}$, and its complement be $y$. Then $y + \theta_2=90^{\circ}$.

Step4: Solve for the complement

$y=90^{\circ}-62^{\circ}=28^{\circ}$.

Answer:

(a) $109^{\circ}$
(b) $28^{\circ}$