Question

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

Explanation:

Step1: Find x using corresponding angles

Since \( m \parallel n \), the angle \( x^\circ \) and the \( 41^\circ \) angle are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So, \( x = 41 \).

Step2: Find y using supplementary angles

The angle \( y^\circ \) and the \( 41^\circ \) angle are supplementary (they form a linear pair, so their sum is \( 180^\circ \)). So, \( y + 41 = 180 \). Solving for \( y \), we get \( y = 180 - 41 = 139 \).

Answer:

\( x = 41 \), \( y = 139 \)