Question

find the measure of angle 5.

Explanation:

Step1: Use the property of vertical angles and parallel lines

Since the two lines are parallel, \(5x + 203\) and \(-6x - 42\) are supplementary angles. So, \((5x + 203)+(-6x - 42)=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation: \(5x+203 - 6x - 42=180\), which becomes \(-x+161 = 180\). Then, \(-x=180 - 161\), so \(-x = 19\), and \(x=-19\).

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

First, find the measure of \(5x + 203\). Substitute \(x = - 19\) into \(5x+203\): \(5\times(-19)+203=-95 + 203 = 108\). Since \(\angle5\) and \(5x + 203\) are vertical angles, \(\angle5=108\).

Answer:

\(108\)