Question

1. m∠mpq______

Explanation:

Step1: Set up equation using vertical - angle property

Since vertical angles are equal, we have $5x=3x + 50$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $5x-3x=3x + 50-3x$, which simplifies to $2x=50$. Then divide both sides by 2: $x = 25$.

Step3: Find the measure of $\angle MPQ$

Substitute $x = 25$ into the expression for $\angle MPQ$ which is $3x+50$. So, $m\angle MPQ=3\times25 + 50=75 + 50=125^{\circ}$.

Answer:

$125^{\circ}$