Question

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

(image of a quadrilateral with two adjacent angles labeled 5x° and 4x°, and two pairs of congruent sides indicated by tick marks)

Explanation:

Step1: Identify the figure type

The figure has two pairs of equal - length sides (marked with tick marks), so it is a parallelogram. In a parallelogram, consecutive angles are supplementary, which means their sum is \( 180^\circ \). So we have the equation \( 5x + 4x=180 \).

Step2: Solve for \( x \)

Combine like terms in the equation \( 5x + 4x = 180 \). We get \( 9x=180 \). Divide both sides of the equation by 9: \( x=\frac{180}{9}=20 \).

Step3: Find the measure of each angle

For the angle with measure \( 5x^\circ \), substitute \( x = 20 \) into \( 5x \). We have \( 5\times20 = 100^\circ \).
For the angle with measure \( 4x^\circ \), substitute \( x = 20 \) into \( 4x \). We have \( 4\times20=80^\circ \).

Answer:

\( x = 20 \), \( 5x = 100^\circ \), \( 4x = 80^\circ \)