Question

solve for x. diagram: horizontal line ( ekd ) (arrows at ( e ) and ( d )), vertical lines ( fjg ) (arrows at ( f ) and ( g )) and ( hki ) (arrows at ( h ) and ( i )) intersecting ( ekd ) at ( j ) and ( k ), respectively. angle at ( k ): ( (7x + 7)^circ ), angle at ( j ): ( (10x - 26)^circ ). \save answer\ box with ( x = ) blank.

Explanation:

Step1: Identify the relationship

Since lines \( FH \) and \( GI \) are parallel (indicated by the arrows), and \( ED \) is a transversal, the alternate interior angles \( \angle JK G \) (which is \( (10x - 26)^\circ \)) and \( \angle I K E \) (which is \( (7x + 7)^\circ \)) are equal. So we set up the equation:
\( 10x - 26 = 7x + 7 \)

Step2: Solve for \( x \)

Subtract \( 7x \) from both sides:
\( 10x - 7x - 26 = 7x - 7x + 7 \)
\( 3x - 26 = 7 \)

Add 26 to both sides:
\( 3x - 26 + 26 = 7 + 26 \)
\( 3x = 33 \)

Divide both sides by 3:
\( \frac{3x}{3} = \frac{33}{3} \)
\( x = 11 \)

Answer:

\( 11 \)