Question

(a) an angle measures 53°. what is the measure of its complement? (b) an angle measures 45°. what is the measure of its supplement? measure of the complement: measure of the supplement:

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to 90°. Let the given angle be $\theta = 53^{\circ}$. The measure of its complement $\alpha$ is given by $\alpha=90^{\circ}-\theta$.
$\alpha = 90^{\circ}-53^{\circ}=37^{\circ}$

Step2: Recall the definition of supplementary angles

Supplementary angles add up to 180°. Let the given angle be $\beta = 45^{\circ}$. The measure of its supplement $\gamma$ is given by $\gamma = 180^{\circ}-\beta$.
$\gamma=180^{\circ}-45^{\circ}=135^{\circ}$

Answer:

measure of the complement: $37^{\circ}$
measure of the supplement: $135^{\circ}$