Question

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

Explanation:

Step1: Identify Alternate Interior Angles

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (8x + 6)^\circ \) and \( (4x + 30)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So we set up the equation:
\( 8x + 6 = 4x + 30 \)

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:
\( 8x - 4x + 6 = 30 \)
\( 4x + 6 = 30 \)

Subtract 6 from both sides:
\( 4x = 30 - 6 \)
\( 4x = 24 \)

Divide both sides by 4:
\( x = \frac{24}{4} \)
\( x = 6 \)

Answer:

\( x = 6 \)