Question

(a) an angle measures 149°. what is the measure of its supplement? (b) an angle measures 42°. what is the measure of its complement? measure of the supplement: measure of the complement:

Explanation:

Step1: Find the supplement of \(149^{\circ}\)

The sum of an angle and its supplement is \(180^{\circ}\). Let the supplement be \(x\). Then \(x + 149^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-149^{\circ}\).

Step2: Calculate \(180 - 149\)

\(180-149 = 31\)

Step3: Find the complement of \(42^{\circ}\)

The sum of an angle and its complement is \(90^{\circ}\). Let the complement be \(y\). Then \(y+42^{\circ}=90^{\circ}\), so \(y = 90^{\circ}-42^{\circ}\).

Step4: Calculate \(90 - 42\)

\(90 - 42=48\)

Answer:

measure of the supplement: \(31^{\circ}\)
measure of the complement: \(48^{\circ}\)