Question

find the value of x. then find the measure of each labeled angle.

Explanation:

Step1: Recall parallelogram property

In a parallelogram, adjacent - angles are supplementary, that is, they add up to 180°.
So, \(4x + 8x=180\).

Step2: Combine like - terms

Add the terms on the left - hand side of the equation: \(12x = 180\).

Step3: Solve for \(x\)

Divide both sides of the equation by 12: \(x=\frac{180}{12}=15\).

Step4: Find the measure of the angles

One angle is \(4x\), so \(4\times15 = 60^{\circ}\), and the other is \(8x\), so \(8\times15=120^{\circ}\).

Answer:

\(x = 15\)