Question

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

Explanation:

Step1: Use linear - pair property

Since $(6x - 12)^{\circ}$ and $(9x + 12)^{\circ}$ are a linear - pair, their sum is $180^{\circ}$. So, $(6x-12)+(9x + 12)=180$.
Combining like terms: $6x+9x-12 + 12=180$, which simplifies to $15x=180$.
Dividing both sides by 15: $x=\frac{180}{15}=12$.

Step2: Find the value of $y$

Since $m\parallel n$, the angle $y^{\circ}$ and $(9x + 12)^{\circ}$ are corresponding angles.
Substitute $x = 12$ into $(9x + 12)$: $9\times12+12=108 + 12=120$.
So, $y = 120$.

Answer:

$x = 12$
$y = 120$