Question

(a) an angle measures 145°. what is the measure of its supplement? (b) an angle measures 39°. what is the measure of its complement? measure of the supplement: measure of the complement:

Explanation:

Step1: Find the supplement of \(145^{\circ}\)

Supplementary angles add up to \(180^{\circ}\). Let the supplement be \(x\). Then \(x + 145^{\circ}=180^{\circ}\). Solving for \(x\), we get \(x = 180^{\circ}-145^{\circ}\).

Step2: Calculate \(180^{\circ}-145^{\circ}\)

\(180 - 145=35\), so \(x = 35^{\circ}\).

Step3: Find the complement of \(39^{\circ}\)

Complementary angles add up to \(90^{\circ}\). Let the complement be \(y\). Then \(y+39^{\circ}=90^{\circ}\). Solving for \(y\), we get \(y = 90^{\circ}-39^{\circ}\).

Step4: Calculate \(90^{\circ}-39^{\circ}\)

\(90 - 39 = 51\), so \(y=51^{\circ}\).

Answer:

measure of the supplement: \(35^{\circ}\)
measure of the complement: \(51^{\circ}\)