Question

answer attempt 1 out of 2
x =
y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $2x + 7=3x - 15$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $7=x - 15$. Then add 15 to both sides, $x=22$.

Step3: Use linear - pair property

The angles $(y + 16)^{\circ}$ and $(3x - 15)^{\circ}$ form a linear - pair, so $(y + 16)+(3x - 15)=180$.

Step4: Substitute $x = 22$ into the equation

$(y + 16)+(3\times22 - 15)=180$. First, calculate $3\times22-15=66 - 15 = 51$. Then the equation becomes $y + 16+51=180$, or $y+67 = 180$.

Step5: Solve for $y$

Subtract 67 from both sides, $y = 113$.

Answer:

$x = 22$
$y = 113$