Question

1. (1pt)

(a) an angle measures 132°. what is the measure of its supplement?
(b) an angle measures 53°. what is the measure of its complement?

Explanation:

Step1: Recall supplement - angle formula

The sum of an angle and its supplement is 180°. Let the given angle be $\theta = 132^{\circ}$, and its supplement be $x$. Then $\theta+x = 180^{\circ}$, so $x=180^{\circ}-\theta$.

Step2: Calculate the supplement

Substitute $\theta = 132^{\circ}$ into the formula: $x = 180^{\circ}-132^{\circ}=48^{\circ}$.

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the given angle be $\alpha = 53^{\circ}$, and its complement be $y$. Then $\alpha + y=90^{\circ}$, so $y = 90^{\circ}-\alpha$.

Step4: Calculate the complement

Substitute $\alpha = 53^{\circ}$ into the formula: $y=90^{\circ}-53^{\circ}=37^{\circ}$.

Answer:

(a) 48
(b) 37