Question

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

Explanation:

Step1: Find \(x\) using vertical - angle property

Vertical angles are equal. So \(x = 51\) (since \(x\) and the \(51^{\circ}\) angle are vertical angles).

Step2: Find \(y\) using linear - pair property

\(x + y=180^{\circ}\) (linear pair of angles). Substitute \(x = 51\) into the equation: \(51 + y=180\). Then \(y=180 - 51\).

Answer:

\(x = 51\), \(y = 129\)