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 \(137^{\circ}\) are corresponding angles.
By the Corresponding Angles Postulate, \(x = 137\).

Step2: Find the value of \(y\)

\(x\) and \(y\) are supplementary angles (they form a linear - pair).
Using the formula \(x + y=180^{\circ}\), substitute \(x = 137\) into it: \(137 + y=180\).
Solve for \(y\): \(y=180 - 137=43\).

Answer:

$x = 137$, $y = 43$