Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $9x + 4=7x + 16$.

Step2: Solve the equation for x

Subtract $7x$ from both sides: $9x-7x + 4=7x-7x + 16$, which simplifies to $2x+4 = 16$. Then subtract 4 from both sides: $2x+4 - 4=16 - 4$, getting $2x=12$. Divide both sides by 2: $x=\frac{12}{2}=6$.

Step3: Use linear - pair property

$(9x + 4)+(y + 3)=180$ (since they form a linear - pair). Substitute $x = 6$ into $9x+4$: $9\times6+4=54 + 4=58$. Then the equation becomes $58+(y + 3)=180$. Combine like - terms: $y+61 = 180$. Subtract 61 from both sides: $y=180 - 61=119$.

Answer:

$x = 6$
$y = 119$