Question

answer attempt 1 out of 2
x =
y =

Explanation:

Step1: Use angle - relationship

The angles $(6x - 12)^{\circ}$ and $(9x + 12)^{\circ}$ are supplementary (a linear - pair of angles), so their sum is $180^{\circ}$.
$(6x-12)+(9x + 12)=180$

Step2: Simplify the equation

Combine like - terms: $6x+9x-12 + 12=180$, which simplifies to $15x=180$.

Step3: Solve for x

Divide both sides of the equation $15x = 180$ by 15: $x=\frac{180}{15}=12$.

Step4: Find the value of y

The angle $y^{\circ}$ and $(9x + 12)^{\circ}$ are vertical angles, so they are equal. Substitute $x = 12$ into $(9x + 12)$: $9\times12+12=108 + 12=120$. So $y = 120$.

Answer:

$x = 12$
$y = 120$