Question

(a) an angle measures 40°. what is the measure of its complement? (b) an angle measures 68°. what is the measure of its supplement? measure of the complement: ° measure of the supplement: °

Explanation:

Step1: Recall complement - angle formula

Complementary angles add up to 90°. Let the given angle be $\alpha = 40^{\circ}$. The measure of its complement $\beta$ is given by $\beta=90^{\circ}-\alpha$.

Step2: Calculate the complement

$\beta = 90^{\circ}-40^{\circ}=50^{\circ}$

Step3: Recall supplement - angle formula

Supplementary angles add up to 180°. Let the given angle be $\gamma = 68^{\circ}$. The measure of its supplement $\delta$ is given by $\delta = 180^{\circ}-\gamma$.

Step4: Calculate the supplement

$\delta=180^{\circ}-68^{\circ}=112^{\circ}$

Answer:

measure of the complement: $50^{\circ}$
measure of the supplement: $112^{\circ}$