Question

(a) an angle measures 44°. what is the measure of its complement? (b) an angle measures 106°. 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 $\theta = 44^{\circ}$. The complement $\alpha$ is given by $\alpha=90^{\circ}-\theta$.
So, $\alpha = 90^{\circ}-44^{\circ}=46^{\circ}$.

Step2: Recall the definition of supplementary angles

Supplementary angles add up to 180°.
Let the given angle be $\beta = 106^{\circ}$. The supplement $\gamma$ is given by $\gamma = 180^{\circ}-\beta$.
So, $\gamma=180^{\circ}- 106^{\circ}=74^{\circ}$.

Answer:

measure of the complement: $46^{\circ}$
measure of the supplement: $74^{\circ}$