Question

use an algebraic equation to find the measures of the two angles described below. begin by letting x represent the degree measure of the angles supplement. the measure of the angle is fifty - nine times greater than its supplement. what is the measure of the supplement? 3° what is the measure of the other angle?

Explanation:

Step1: Set up the equation

Let \(x\) be the measure of the supplement. The measure of the angle is \(59x\). Since supplementary angles add up to \(180^{\circ}\), the equation is \(x + 59x=180\).

Step2: Combine like - terms

Combining the left - hand side of the equation, we get \(60x = 180\).

Step3: Solve for \(x\)

Dividing both sides of the equation by 60, we have \(x=\frac{180}{60}=3\). This is the measure of the supplement.

Step4: Find the measure of the other angle

The other angle is \(59x\). Substituting \(x = 3\) into \(59x\), we get \(59\times3 = 177\).

Answer:

177