Question

solve for x.

Explanation:

Answer:

To solve for \( x \), we recognize that \( LM \parallel NO \) (since they are parallel lines cut by a transversal \( JK \)), so the alternate interior angles \( (5x - 30)^\circ \) and \( (3x)^\circ \) are equal.

Set the angles equal:
\( 5x - 30 = 3x \)

Subtract \( 3x \) from both sides:
\( 2x - 30 = 0 \)

Add 30 to both sides:
\( 2x = 30 \)

Divide by 2:
\( x = 15 \)

So the value of \( x \) is \( \boldsymbol{15} \).