Question

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Explanation:

Step1: Assume m and n are parallel

If m and n are parallel, then the corresponding - angles are equal. So we set up the equation based on the equality of corresponding - angles:
$8x + 2=4x + 10$

Step2: Solve the equation for x

Subtract $4x$ from both sides of the equation:
$8x-4x + 2=4x-4x + 10$
$4x+2 = 10$
Subtract 2 from both sides:
$4x+2 - 2=10 - 2$
$4x=8$
Divide both sides by 4:
$x = 2$

Step3: Find the value of y

If m and n are parallel, then $y$ and $(4x + 10)$ are supplementary angles (linear - pair), so $y+(4x + 10)=180$.
Substitute $x = 2$ into $4x + 10$:
$4x+10=4\times2 + 10=8 + 10 = 18$
Then $y=180-(4x + 10)=180 - 18=162$

Answer:

$x = 2,y = 162$