Question

current skill
find the measure of angle 5.
label optional

Explanation:

Step1: Use the property of corresponding angles

Since the two horizontal lines are parallel, \(-6x + 164\) and \(2x+68\) are equal. So, \(-6x + 164=2x + 68\).

Step2: Solve the equation for \(x\)

Add \(6x\) to both sides: \(164 = 8x+68\).
Subtract \(68\) from both sides: \(96 = 8x\).
Divide both sides by \(8\): \(x = 12\).

Step3: Find the measure of \(\angle5\)

First, find the measure of \(\angle2\) by substituting \(x = 12\) into \(2x+68\): \(2\times12 + 68=24 + 68 = 92\).
Since \(\angle2\) and \(\angle5\) are supplementary (their sum is \(180^{\circ}\)), \(\angle5=180 - 92=88^{\circ}\).

Answer:

\(88^{\circ}\)