Question

(1) an angle measures 25°. what is the measure of its complement? (2) an angle measures 40°. what is the measure of its supplement?

Explanation:

Step1: Recall complement formula

The sum of an angle and its complement is 90°. Let the given angle be $\alpha = 25^{\circ}$, and the complement be $\beta$. Then $\alpha+\beta = 90^{\circ}$, so $\beta=90^{\circ}-\alpha$.

Step2: Calculate the complement

Substitute $\alpha = 25^{\circ}$ into the formula: $\beta = 90^{\circ}-25^{\circ}=65^{\circ}$.

Step3: Recall supplement formula

The sum of an angle and its supplement is 180°. Let the given angle be $\gamma = 40^{\circ}$, and the supplement be $\delta$. Then $\gamma+\delta = 180^{\circ}$, so $\delta = 180^{\circ}-\gamma$.

Step4: Calculate the supplement

Substitute $\gamma = 40^{\circ}$ into the formula: $\delta=180^{\circ}-40^{\circ}=140^{\circ}$.

Answer:

measure of the complement: $65^{\circ}$
measure of the supplement: $140^{\circ}$