Question

type the correct answer in each box.
parallel lines ( p ) and ( q ) are cut by two non - parallel lines, ( m ) and ( n ), as shown in the figure.
the value of ( x ) is ( ) degrees, and the value of ( y ) is ( ) degrees.

Explanation:

Step1: Find the value of \(x\)

When two parallel lines are cut by a transversal, alternate - interior angles are equal. Here, \(x\) and the angle of \(102^{\circ}\) are alternate - interior angles. So \(x = 102^{\circ}\)

Step2: Find the value of \(y\)

When two parallel lines are cut by a transversal, consecutive - interior angles are supplementary. The angle adjacent to \(y\) and the \(115^{\circ}\) angle are consecutive - interior angles.
Let the angle adjacent to \(y\) be \(z\). Then \(z=115^{\circ}\) (alternate - interior angles).
Since \(y + z=180^{\circ}\) (linear pair), \(y = 180 - 115\)
\(y=65^{\circ}\)

Answer:

The value of \(x\) is \(102\) degrees, and the value of \(y\) is \(65\) degrees.