Question

(a) an angle measures 46°. what is the measure of its complement? (b) an angle measures 74°. what is the measure of its supplement? measure of the complement: ° measure of the supplement: °

Explanation:

Step1: Recall complement - angle formula

Complementary angles add up to 90°. Let the given angle be $\theta = 46^{\circ}$. The measure of its complement $x$ is given by $x=90^{\circ}-\theta$.

Step2: Calculate the complement

$x = 90^{\circ}-46^{\circ}=44^{\circ}$.

Step3: Recall supplement - angle formula

Supplementary angles add up to 180°. Let the given angle be $\alpha = 74^{\circ}$. The measure of its supplement $y$ is given by $y = 180^{\circ}-\alpha$.

Step4: Calculate the supplement

$y=180^{\circ}-74^{\circ}=106^{\circ}$.

Answer:

measure of the complement: $44^{\circ}$
measure of the supplement: $106^{\circ}$