Question

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

Explanation:

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

Vertical angles are equal. The angle of \(133^{\circ}\) and \(y\) are not vertical angles, but \(x\) and the angle adjacent to \(133^{\circ}\) form a linear pair. Wait, no, actually, \(x\) and \(133^{\circ}\) are vertical angles. So \(x = 133^{\circ}\) is wrong. Wait, no, \(x\) and \(133^{\circ}\) are not vertical angles. Wait, \(x\) and the angle adjacent to \(133^{\circ}\) (let's call it \(z\)): \(z + 133^{\circ}=180^{\circ}\) (linear pair). But \(x\) and \(z\) are vertical angles. Wait, no, \(x\) and \(133^{\circ}\) are supplementary (linear pair). So \(x+133^{\circ}=180^{\circ}\), then \(x = 180 - 133=47^{\circ}\)

Step2: Find \(y\) using vertical - angle property

\(y\) and \(133^{\circ}\) are vertical angles. By the vertical - angle theorem (when two lines intersect, vertical angles are equal), \(y = 133^{\circ}\)

Answer:

\(x = 47\), \(y = 133\)