Question

(a) an angle measures 142°. what is the measure of its supplement? (b) an angle measures 65°. what is the measure of its complement? measure of the supplement: measure of the complement:

Explanation:

Step1: Recall supplement - angle formula

Supplementary angles add up to 180°. Let the given angle be $\alpha = 142^{\circ}$, and its supplement be $\beta$. Then $\alpha+\beta = 180^{\circ}$, so $\beta=180^{\circ}-\alpha$.

Step2: Calculate the supplement

$\beta = 180^{\circ}-142^{\circ}=38^{\circ}$

Step3: Recall complement - angle formula

Complementary angles add up to 90°. Let the given angle be $\gamma = 65^{\circ}$, and its complement be $\delta$. Then $\gamma+\delta = 90^{\circ}$, so $\delta = 90^{\circ}-\gamma$.

Step4: Calculate the complement

$\delta=90^{\circ}-65^{\circ}=25^{\circ}$

Answer:

measure of the supplement: $38^{\circ}$
measure of the complement: $25^{\circ}$