Question

find the measure of angle 5.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(-5x + 200=3x + 72\)

Step2: Solve the equation for \(x\)

Add \(5x\) to both sides: \(200 = 8x+72\)
Subtract \(72\) from both sides: \(128 = 8x\)
Divide both sides by \(8\): \(x = 16\)

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

First, find the measure of \(\angle4\) using \(3x + 72\). Substitute \(x = 16\): \(3\times16+72=48 + 72=120\)
Since \(\angle4\) and \(\angle5\) are supplementary (\(\angle4+\angle5 = 180^{\circ}\))
\(\angle5=180 - 120=60^{\circ}\)

Answer:

\(60^{\circ}\)