Question

(a) an angle measures 26°. what is the measure of its complement? (b) an angle measures 143°. what is the measure of its supplement? measure of the complement: measure of the supplement:

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). Let the complement of \(26^{\circ}\) be \(x\). Then \(x + 26^{\circ}=90^{\circ}\).

Step2: Solve for \(x\)

\(x=90^{\circ}-26^{\circ}=64^{\circ}\)

Step3: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\). Let the supplement of \(143^{\circ}\) be \(y\). Then \(y + 143^{\circ}=180^{\circ}\).

Step4: Solve for \(y\)

\(y=180^{\circ}-143^{\circ}=37^{\circ}\)

Answer:

measure of the complement: \(64^{\circ}\)
measure of the supplement: \(37^{\circ}\)