Question

∠m measures 31°. (a) find the supplement of ∠m. (b) find the complement of ∠m. (a) the supplement of ∠m is

Explanation:

Step1: Recall supplement - angle formula

The sum of an angle and its supplement is 180°. Let the measure of ∠M be \(m\angle M = 31^{\circ}\), and the supplement be \(x\). Then \(x + m\angle M=180^{\circ}\).

Step2: Solve for the supplement

Substitute \(m\angle M = 31^{\circ}\) into the equation \(x + 31^{\circ}=180^{\circ}\), so \(x=180^{\circ}-31^{\circ}=149^{\circ}\).

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the complement be \(y\). Then \(y + m\angle M = 90^{\circ}\).

Step4: Solve for the complement

Substitute \(m\angle M = 31^{\circ}\) into the equation \(y+31^{\circ}=90^{\circ}\), so \(y = 90^{\circ}-31^{\circ}=59^{\circ}\).

Answer:

(a) 149°
(b) 59°