Question

(a) an angle measures 26°. what is the measure of its complement? (b) an angle measures 40°. what is the measure of its supplement?

Explanation:

Step1: Recall complement - angle formula

Complementary angles add up to 90°. Let the given angle be $\alpha = 26^{\circ}$, and its complement be $\beta$. Then $\alpha+\beta = 90^{\circ}$.

Step2: Calculate the complement

$\beta=90^{\circ}-\alpha = 90^{\circ}-26^{\circ}=64^{\circ}$.

Step3: Recall supplement - angle formula

Supplementary angles add up to 180°. Let the given angle be $\gamma = 40^{\circ}$, and its supplement be $\delta$. Then $\gamma+\delta = 180^{\circ}$.

Step4: Calculate the supplement

$\delta = 180^{\circ}-\gamma=180^{\circ}-40^{\circ}=140^{\circ}$.

Answer:

(a) 64°
(b) 140°