Question

the measure of an angle is seventeen times the measure of its supplementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Set up the equation

Let the measure of the supplementary angle be \(x\). Then the measure of the other angle is \(17x\). Since supplementary angles add up to \(180^{\circ}\), we have the equation \(x + 17x=180\).

Step2: Solve the equation

Combine like terms: \(18x = 180\).
Divide both sides by \(18\): \(x=\frac{180}{18}=10\).

Step3: Find the measure of the other angle

If \(x = 10\), then \(17x=17\times10 = 170\).

Answer:

\(10\) and \(170\)