Question

use the image below to find the requested values. find the measure of ∠gfy. label optional 39 what is the value of r?

Explanation:

Step1: Note angle - relationship

We know that \(\angle GFM\) is a straight - angle, so \(\angle GFY+\angle YFM = 180^{\circ}\). Given \(\angle YFM = 51^{\circ}\), and \(\angle GFY=(r - 66)^{\circ}\).

Step2: Set up equation

\((r - 66)+51 = 180\).

Step3: Simplify the left - hand side of the equation

\(r-66 + 51=r - 15\). So the equation becomes \(r-15 = 180\).

Step4: Solve for \(r\)

Add 15 to both sides of the equation: \(r=180 + 15\).

Answer:

\(r = 195\)