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 \(47^{\circ}\) are alternate - interior angles.
By the alternate - interior angles theorem, \(x = 47\)

Step2: Find the value of \(y\)

Since \(x\) and \(y\) are supplementary angles (\(x + y=180^{\circ}\))
Substitute \(x = 47\) into \(x + y = 180\), we get \(47+y=180\)
Solve for \(y\): \(y=180 - 47=133\)

Answer:

$x = 47$, $y = 133$