Question

find the measure of ∠mpq. m∠mpq =

Explanation:

Step1: Identify angle - relationship

Assume $LM\parallel NO$. Then $\angle MPQ$ and $\angle NQK$ are corresponding angles, so $10x + 28=52 - 2x$.

Step2: Solve for $x$

Add $2x$ to both sides: $10x+2x + 28=52-2x + 2x$, which simplifies to $12x+28 = 52$. Then subtract 28 from both sides: $12x+28 - 28=52 - 28$, getting $12x=24$. Divide both sides by 12: $x = 2$.

Step3: Find $\angle MPQ$

Substitute $x = 2$ into the expression for $\angle MPQ$. $\angle MPQ=10x + 28$. So $\angle MPQ=10\times2+28=20 + 28=48^{\circ}$.

Answer:

$48$