Question

given m || n, find the value of x and y.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle of 142° and $x$ are vertical angles. So $x = 142$.
$x=142$

Step2: Use supplementary - angle property

Since $x$ and $y$ are supplementary angles (linear - pair), and the sum of supplementary angles is 180°. So $y=180 - x$.
Substitute $x = 142$ into the equation: $y=180 - 142=38$.

Answer:

$x = 142$, $y = 38$