Question

find m∠vpq.

Explanation:

Step1: Set up equation

Since the two - given angles are vertical angles, they are equal. So we set up the equation $2x + 25=x + 50$.
$2x+25=x + 50$

Step2: Solve for x

Subtract x from both sides: $2x - x+25=x - x + 50$, which simplifies to $x+25 = 50$. Then subtract 25 from both sides: $x=50 - 25$, so $x = 25$.

Step3: Find the measure of ∠VPQ

Substitute $x = 25$ into the expression for $\angle VPQ$ which is $2x+25$. So $2(25)+25=50 + 25=75^{\circ}$.

Answer:

$75^{\circ}$