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: \(12x = 180\). Then divide both sides by \(12\): \(x=\frac{180}{12}=15\).

Step3: Find the other angle

The other angle is \(11x\). Substitute \(x = 15\) into \(11x\), we get \(11\times15 = 165\).

Answer:

\(15\) and \(165\)