Question

given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify the angle relationship

Since \( m \parallel n \) and the transversal \( t \) intersects them, the angles \( (3x + 25)^\circ \) and \( (6x - 5)^\circ \) are alternate interior angles. Alternate interior angles are equal when two parallel lines are cut by a transversal. So we set up the equation:
\( 3x + 25 = 6x - 5 \)

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\( 25 = 3x - 5 \)

Add 5 to both sides:
\( 30 = 3x \)

Divide both sides by 3:
\( x = 10 \)

Answer:

\( x = 10 \)