Question

segments and angles
finding supplementary and complementary angles
(a) an angle measures 65°. what is the measure of its complement?
(b) an angle measures 89°. 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 $\theta = 65^{\circ}$, and the complement be $x$. Then $x+65^{\circ}=90^{\circ}$, so $x = 90^{\circ}-65^{\circ}$.
$x=90 - 65=25^{\circ}$

Step2: Recall the definition of supplementary angles

Supplementary angles add up to 180°. Let the given angle be $\theta = 89^{\circ}$, and the supplement be $y$. Then $y + 89^{\circ}=180^{\circ}$, so $y=180^{\circ}-89^{\circ}$.
$y = 180-89 = 91^{\circ}$

Answer:

measure of the complement: $25^{\circ}$
measure of the supplement: $91^{\circ}$