Question

the measure of an angle is eleven 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 \(11x\). Since supplementary angles sum to \(180^{\circ}\), we have \(x + 11x=180\).

Step2: Solve the equation

Combine like - terms: \(12x = 180\). Divide both sides by 12: \(x=\frac{180}{12}=15\).

Step3: Find the measure of the other angle

If \(x = 15\), then \(11x=11\times15 = 165\).

Answer:

\(15\) and \(165\)