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 \( (7x + 9)^\circ \) and \( (8x - 8)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So we set up the equation:
\( 7x + 9 = 8x - 8 \)

Step2: Solve for \( x \)

Subtract \( 7x \) from both sides:
\( 7x + 9 - 7x = 8x - 8 - 7x \)
\( 9 = x - 8 \)

Then add 8 to both sides:
\( 9 + 8 = x - 8 + 8 \)
\( 17 = x \)

Answer:

\( x = 17 \)