Question

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

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), \(x\) and the \(41^{\circ}\) angle are corresponding angles.
By the Corresponding Angles Theorem, \(x = 41\)

Step2: Find the value of \(y\)

Since \(x\) and \(y\) are supplementary angles (they form a linear pair), \(x + y=180\)
Substitute \(x = 41\) into the equation: \(41 + y=180\)
Solve for \(y\): \(y=180 - 41=139\)

Answer:

$x = 41$, $y = 139$