Question

solve for x.

x = \square

Explanation:

Step1: Identify angle relationship

Since \( GH \parallel IJ \) and \( EF \) is a transversal, the angles \( (9x + 39)^\circ \) and \( (11x + 61)^\circ \) are same - side interior angles. Same - side interior angles are supplementary, so their sum is \( 180^\circ \).
We can write the equation: \( (9x + 39)+(11x + 61)=180 \)

Step2: Simplify the left - hand side of the equation

Combine like terms: \( 9x+11x + 39 + 61=180 \)
\( 20x+100 = 180 \)

Step3: Solve for x

Subtract 100 from both sides of the equation: \( 20x=180 - 100 \)
\( 20x = 80 \)
Divide both sides by 20: \( x=\frac{80}{20}=4 \)

Answer:

\( x = 4 \)