Question

find the measure of ∠mpq. (4x + 12)° (5x - 18)° m∠mpq =

Explanation:

Step1: Identify angle - relationship

Since $\angle MPQ$ and $\angle NQK$ are corresponding angles (assuming $LM\parallel NO$), they are equal. So $4x + 12=5x - 18$.

Step2: Solve for $x$

Subtract $4x$ from both sides: $12=x - 18$. Then add 18 to both sides, we get $x=30$.

Step3: Find $\angle MPQ$

Substitute $x = 30$ into the expression for $\angle MPQ$ which is $4x+12$. So $\angle MPQ=4\times30 + 12=120 + 12=132^{\circ}$.

Answer:

$132$