Question

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

x = 30; both labeled angles are 150°.
x = 30; both labeled angles are 120°.
x = 20; both labeled angles are 90°.
x = 20; the labeled angles are 80° and 100°.

Explanation:

Step1: Use the property of a parallelogram

In a parallelogram, consecutive angles are supplementary. So, \(5x + 4x=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(9x = 180\). Then, divide both sides by 9: \(x=\frac{180}{9}=20\).

Step3: Calculate the measures of the angles

Substitute \(x = 20\) into \(4x\) and \(5x\). For \(4x\), we have \(4\times20 = 80\). For \(5x\), we have \(5\times20=100\).

Answer:

\(x = 20\); the labeled angles are \(80^{\circ}\) and \(100^{\circ}\)