Question

given ( mparallel n ), find the value of ( x ).

Explanation:

Step1: Identify same-side interior angles

When transversal \( t \) cuts parallel lines \( m \) and \( n \), the angles \( (5x - 16)^\circ \) and \( (6x + 9)^\circ \) are same-side interior angles, so they are supplementary.

Step2: Set up the equation

\( (5x - 16) + (6x + 9) = 180 \)

Step3: Simplify the left side

\( 11x - 7 = 180 \)

Step4: Solve for \( x \)

\( 11x = 187 \)
\( x = \frac{187}{11} = 17 \)

Answer:

17