Question

1. find the m∠opm, if m∠opm=(2y + 11)°, and m∠lpm=(8y - 7)°.

Explanation:

Step1: Assume angle - bisector condition

Since no other information is given, assume $\overrightarrow{PM}$ is the angle - bisector of $\angle OPL$, so $m\angle OPM=m\angle LPM$.
$2y + 11=8y-7$

Step2: Solve the equation for $y$

Subtract $2y$ from both sides: $11 = 8y-2y - 7$, which simplifies to $11=6y - 7$.
Add 7 to both sides: $11 + 7=6y$, so $18 = 6y$.
Divide both sides by 6: $y=\frac{18}{6}=3$.

Step3: Find $m\angle OPM$

Substitute $y = 3$ into the expression for $m\angle OPM$.
$m\angle OPM=2y + 11=2\times3+11=6 + 11=17^{\circ}$

Answer:

$17^{\circ}$