Question

find the values of the variables.
$x =
$y =
(simplify your answer.)

Explanation:

Step1: Use property of same - side interior angles

For the pair of same - side interior angles with measures $3x^{\circ}$ and $(x - 16)^{\circ}$, since they are supplementary (sum to $180^{\circ}$), we have the equation $3x+(x - 16)=180$.
Combining like - terms: $3x+x-16 = 180$, which simplifies to $4x-16 = 180$.
Adding 16 to both sides: $4x=180 + 16=196$.
Dividing both sides by 4: $x=\frac{196}{4}=49$.

Step2: Use property of same - side interior angles for y

For the pair of same - side interior angles with measures $2y^{\circ}$ and $(y + 12)^{\circ}$, since they are supplementary (sum to $180^{\circ}$), we have the equation $2y+(y + 12)=180$.
Combining like - terms: $2y+y+12 = 180$, which simplifies to $3y+12 = 180$.
Subtracting 12 from both sides: $3y=180 - 12 = 168$.
Dividing both sides by 3: $y=\frac{168}{3}=56$.

Answer:

$x = 49$
$y = 56$