Question

find the measure of ∠mpo.
m∠mpo = □°

Explanation:

Step1: Identify angle - relationship

Assume $KL\parallel MN$. Then, $\angle MPO$ and $\angle POL$ are corresponding angles, so $8x - 5=65 - 2x$.

Step2: Solve for $x$

Add $2x$ to both sides: $8x+2x - 5=65 - 2x+2x$, which simplifies to $10x - 5 = 65$. Then add 5 to both sides: $10x-5 + 5=65 + 5$, getting $10x=70$. Divide both sides by 10: $x = 7$.

Step3: Find $\angle MPO$

Substitute $x = 7$ into the expression for $\angle MPO$. $\angle MPO=(8x - 5)^{\circ}$. So, $\angle MPO=8\times7 - 5=56 - 5=51^{\circ}$.

Answer:

$51$