Question

find the measure of angle 1,

Explanation:

Step1: Set up equation

Since the two angles \(8x - 4\) and \(6x+8\) are equal (alternate - interior angles for parallel lines), we have \(8x - 4=6x + 8\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(8x-6x-4 = 6x - 6x+8\), \(2x-4 = 8\). Add \(4\) to both sides: \(2x-4 + 4=8 + 4\), \(2x=12\). Divide by \(2\): \(x = 6\).

Step3: Find angle measure

Substitute \(x = 6\) into \(6x + 8\): \(6\times6+8=36 + 8=44^{\circ}\). Angle \(1\) and \(44^{\circ}\) are supplementary (linear - pair), so angle \(1=180^{\circ}-44^{\circ}=136^{\circ}\).

Answer:

\(136^{\circ}\)