Question

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

Explanation:

Step1: Find the supplementary angle to \( 142^\circ \) for \( x \)

Since \( m \parallel n \), the angle adjacent to \( 142^\circ \) and \( x^\circ \) are supplementary (they form a linear pair with the transversal). So, \( x + 142 = 180 \).
Solving for \( x \): \( x = 180 - 142 = 38 \).

Step2: Determine \( y \) using vertical or corresponding angles

\( y \) and the \( 142^\circ \) angle are corresponding angles (or vertical angles, depending on the transversal), so \( y = 142 \) (because when two parallel lines are cut by a transversal, corresponding angles are equal, and vertical angles are also equal).

Answer:

\( x = 38 \), \( y = 142 \)