Question

given ( m parallel n ), find the value of ( x ). the diagram shows two parallel lines ( m ) and ( n ) cut by a transversal ( t ), with one angle labeled ( (6x + 30)^circ ) on line ( m ) and another angle labeled ( (8x - 10)^circ ) on line ( n ).

Explanation:

Step1: Identify the angle relationship

Since \( m \parallel n \) and the transversal \( t \) intersects them, the given angles \( (6x + 30)^\circ \) and \( (8x - 10)^\circ \) are alternate interior angles. Alternate interior angles are equal when two parallel lines are cut by a transversal. So we set up the equation:
\( 6x + 30 = 8x - 10 \)

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\( 30 = 2x - 10 \)

Add 10 to both sides:
\( 40 = 2x \)

Divide both sides by 2:
\( x = 20 \)

Answer:

\( x = 20 \)