Question

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

Explanation:

Step1: Find the value of \(x\)

Since \(x\) and \(51^{\circ}\) are supplementary angles (they form a linear pair), we use the formula \(x+51^{\circ}=180^{\circ}\).
So, \(x = 180^{\circ}- 51^{\circ}=129^{\circ}\).

Step2: Find the value of \(y\)

Since \(m\parallel n\), \(y\) and \(51^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal.
So, \(y = 51^{\circ}\).

Answer:

$x = 129$, $y = 51$