Question

problem 20. lesson 16) two angles are supplementary. the measure of one angle is 1.5 times the measure of the other angle. what are the measures of both angles?

Explanation:

Step1: Set up variables

Let one angle be \(x\). Then the other angle is \(1.5x\).

Step2: Use the supplementary - angle property

Since supplementary angles sum to \(180^{\circ}\), we have \(x + 1.5x=180\).
Combine like terms: \(2.5x = 180\).
Solve for \(x\): \(x=\frac{180}{2.5}=72\).

Step3: Find the other angle

Substitute \(x = 72\) into \(1.5x\). So \(1.5\times72 = 108\).

Answer:

The measures of the angles are \(72^{\circ}\) and \(108^{\circ}\).