Question

Question was provided via image upload.

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $3x - 16=5x - 110$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $- 16 = 5x-3x - 110$.
Simplify to get $-16 = 2x-110$.
Add 110 to both sides: $-16 + 110=2x$, so $94 = 2x$.
Divide both sides by 2: $x = 47$.

Step3: Find the value of one of the vertical angles

Substitute $x = 47$ into $3x - 16$: $3\times47-16=141 - 16=125$.

Step4: Find the value of $y$

Since $y$ and the angle $(3x - 16)$ are supplementary (linear - pair, sum to $180^{\circ}$), $y=180-(3x - 16)$.
Substitute $x = 47$: $y = 180 - 125 = 55$.

Answer:

$x = 47$, $y = 55$