Question

(a) an angle measures 27°. what is the measure of its complement? measure of the complement: (b) an angle measures 90°. what is the measure of its supplement? measure of the supplement:

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to 90°.

Step2: Calculate the complement for part (a)

Let the angle be $\theta = 27^{\circ}$. The complement $\alpha=90^{\circ}-\theta = 90^{\circ}- 27^{\circ}=63^{\circ}$.

Step3: Recall the definition of supplementary angles

Supplementary angles add up to 180°.

Step4: Calculate the supplement for part (a)

The supplement $\beta = 180^{\circ}-\theta=180^{\circ}-27^{\circ}=153^{\circ}$.

Step5: Calculate the supplement for part (b)

Let the angle be $\theta = 90^{\circ}$. The supplement $\gamma=180^{\circ}-\theta = 180^{\circ}-90^{\circ}=90^{\circ}$.

Answer:

(a) Complement: $63^{\circ}$, Supplement: $153^{\circ}$
(b) Supplement: $90^{\circ}$