Question

find the measure of ∠mpq. m∠mpq =

Explanation:

Step1: Set up equation

Since $\angle MPQ$ and $\angle NQK$ are vertical - angles, they are equal. So we set up the equation $4x + 12=5x - 18$.

Step2: Solve for x

Subtract $4x$ from both sides: $4x+12 - 4x=5x - 18-4x$, which gives $12=x - 18$. Then add 18 to both sides: $12 + 18=x-18 + 18$, so $x = 30$.

Step3: Find measure of $\angle MPQ$

Substitute $x = 30$ into the expression for $\angle MPQ$: $m\angle MPQ=4x + 12$. Then $m\angle MPQ=4\times30+12$. Calculate $4\times30+12=120 + 12=132$.

Answer:

$132$