Question

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

Explanation:

Step1: Identify the angle relationship

Since \( m \parallel n \) and the transversal cuts them, the \( 102^\circ \) angle and \( x^\circ \) angle are corresponding angles (or alternate interior angles, depending on the diagram's exact configuration, but in parallel lines with a transversal, corresponding/alternate interior angles are equal when lines are parallel).

Step2: Determine the value of \( x \)

By the property of parallel lines and transversals (corresponding angles are equal), we have \( x = 102 \).

Answer:

\( x = 102 \)