Question

(a) an angle measures 70°. what is the measure of its supplement? (b) an angle measures 49°. what is the measure of its complement? measure of the supplement: measure of the complement:

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\). Let the given angle be \(A = 70^{\circ}\). Let its supplement be \(S\). Then \(A+S = 180^{\circ}\). So \(S=180^{\circ}-A\).
Substitute \(A = 70^{\circ}\) into the formula: \(S = 180^{\circ}-70^{\circ}=110^{\circ}\).

Step2: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). Let the given angle be \(B = 49^{\circ}\). Let its complement be \(C\). Then \(B + C=90^{\circ}\). So \(C = 90^{\circ}-B\).
Substitute \(B = 49^{\circ}\) into the formula: \(C=90^{\circ}-49^{\circ}=41^{\circ}\).

Answer:

measure of the supplement: \(110\)
measure of the complement: \(41\)