Question

(a) an angle measures 138°. what is the measure of its supplement? (b) an angle measures 25°. what is the measure of its complement? measure of the supplement: measure of the complement:

Explanation:

Part (a)

Step1: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\). Let the measure of the supplement be \(x\). Then \(x + 138^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

Subtract \(138^{\circ}\) from both sides: \(x=180^{\circ}- 138^{\circ}\).

$$x = 42^{\circ}$$

Part (b)

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). Let the measure of the complement be \(y\). Then \(y + 25^{\circ}=90^{\circ}\).

Step2: Solve for \(y\)

Subtract \(25^{\circ}\) from both sides: \(y=90^{\circ}-25^{\circ}\).

$$y = 65^{\circ}$$

Answer:

measure of the supplement: \(42\)
measure of the complement: \(65\)