Question

a) an angle measures 106°. what is the measure of its supplement? b) an angle measures 53°. 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 $\theta = 106^{\circ}$, and the supplement be $x$. Then $\theta+x = 180^{\circ}$, so $x=180^{\circ}-\theta$.

Step2: Calculate the supplement

Substitute $\theta = 106^{\circ}$ into the formula: $x = 180^{\circ}-106^{\circ}=74^{\circ}$.

Step3: Recall complement - angle formula

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

measure of the supplement: $74^{\circ}$
measure of the complement: $37^{\circ}$