Question

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

Explanation:

Step1: Use the property of trapezoid

In an isosceles trapezoid, consecutive angles between the bases 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 measure of each angle

For the angle \(5x^{\circ}\), substitute \(x = 20\): \(5\times20^{\circ}=100^{\circ}\).
For the angle \(4x^{\circ}\), substitute \(x = 20\): \(4\times20^{\circ}=80^{\circ}\).

Answer:

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