Question

(a) an angle measures 109°. what is the measure of its supplement? (b) an angle measures 42°. 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 $\theta_1 = 109^{\circ}$, and its supplement be $x$. Then $x=180^{\circ}-\theta_1$.
$x = 180 - 109$

Step2: Calculate the supplement

$x=71^{\circ}$

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the given angle be $\theta_2 = 42^{\circ}$, and its complement be $y$. Then $y = 90^{\circ}-\theta_2$.
$y=90 - 42$

Step4: Calculate the complement

$y = 48^{\circ}$

Answer:

measure of the supplement: $71^{\circ}$
measure of the complement: $48^{\circ}$