Question

(a) an angle measures 56°. what is the measure of its supplement? (b) an angle measures 41°. 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 $\theta = 56^{\circ}$. The measure of its supplement $\alpha$ is given by $\alpha=180^{\circ}-\theta$.

Step2: Calculate the supplement

$\alpha = 180^{\circ}-56^{\circ}=124^{\circ}$

Step3: Recall complement - angle formula

Complementary angles add up to 90°. Let the given angle be $\beta = 41^{\circ}$. The measure of its complement $\gamma$ is given by $\gamma = 90^{\circ}-\beta$.

Step4: Calculate the complement

$\gamma=90^{\circ}-41^{\circ}=49^{\circ}$

Answer:

measure of the supplement: $124^{\circ}$
measure of the complement: $49^{\circ}$