Question

what is the measure of the complement of 75°?
□°
what is the measure of the supplement of 75°?
□°

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). Let the complement of \(75^{\circ}\) be \(x\). Then \(x + 75^{\circ}=90^{\circ}\).

Step2: Solve for \(x\)

\(x=90^{\circ}-75^{\circ}=15^{\circ}\)

Step3: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\). Let the supplement of \(75^{\circ}\) be \(y\). Then \(y + 75^{\circ}=180^{\circ}\).

Step4: Solve for \(y\)

\(y=180^{\circ}-75^{\circ}=105^{\circ}\)

Answer:

The measure of the complement of \(75^{\circ}\) is \(15^{\circ}\). The measure of the supplement of \(75^{\circ}\) is \(105^{\circ}\).