Question

(a) an angle measures 145°. what is the measure of its supplement? (b) an angle measures 43°. what is the measure of its complement? measure of the supplement: measure of the complement:

Explanation:

(a)

Step1: Recall the formula for supplementary angles

Supplementary angles add up to \(180^{\circ}\). Let the angle be \(A = 145^{\circ}\), and its supplement be \(S\). Then \(A+S = 180^{\circ}\).

Step2: Solve for the supplement

\(S=180^{\circ}-A\). Substitute \(A = 145^{\circ}\) into the formula: \(S = 180^{\circ}-145^{\circ}=35^{\circ}\).

(b)

Step1: Recall the formula for complementary angles

Complementary angles add up to \(90^{\circ}\). Let the angle be \(C = 43^{\circ}\), and its complement be \(K\). Then \(C + K=90^{\circ}\).

Step2: Solve for the complement

\(K = 90^{\circ}-C\). Substitute \(C = 43^{\circ}\) into the formula: \(K=90^{\circ}-43^{\circ}=47^{\circ}\).

Answer:

measure of the supplement: \(35^{\circ}\)
measure of the complement: \(47^{\circ}\)