Question

segments and angles finding supplementary and complementary angles (a) an angle measures 39°. what is the measure of its supplement? (b) an angle measures 45°. 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 $\theta = 39^{\circ}$. The measure of its supplement $\alpha$ is given by $\alpha=180^{\circ}-\theta$.

Step2: Calculate the supplement

$\alpha = 180 - 39=141^{\circ}$.

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the given angle be $\beta = 45^{\circ}$. The measure of its complement $\gamma$ is given by $\gamma = 90^{\circ}-\beta$.

Step4: Calculate the complement

$\gamma=90 - 45 = 45^{\circ}$.

Answer:

measure of the supplement: $141^{\circ}$
measure of the complement: $45^{\circ}$