Question

segments and angles finding supplementary and complementary angles (a) an angle measures 45°. what is the measure of its complement? (b) an angle measures 135°. 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 $\theta$. The measure of its complement is $90^{\circ}-\theta$.

Step2: Calculate the complement of 45°

For $\theta = 45^{\circ}$, the measure of its complement is $90^{\circ}-45^{\circ}=45^{\circ}$.

Step3: Recall supplement - angle formula

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

Step4: Calculate the supplement of 135°

For $\alpha = 135^{\circ}$, the measure of its supplement is $180^{\circ}-135^{\circ}=45^{\circ}$.

Answer:

measure of the complement: $45$
measure of the supplement: $45$