Question

1. ∠lmn is a straight angle. find m∠lmp and m∠nmp.

Explanation:

Step1: Use straight - angle property

Since $\angle LMN$ is a straight angle, $m\angle LMP + m\angle NMP=180^{\circ}$. So, $(-16x + 13)+(-20x + 23)=180$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms, we get $(-16x-20x)+(13 + 23)=180$, which simplifies to $-36x+36 = 180$.

Step3: Isolate the variable term

Subtract 36 from both sides: $-36x=180 - 36$, so $-36x=144$.

Step4: Solve for $x$

Divide both sides by - 36: $x=\frac{144}{-36}=-4$.

Step5: Find $m\angle LMP$

Substitute $x = - 4$ into the expression for $m\angle LMP$: $m\angle LMP=-16x + 13=-16\times(-4)+13=64 + 13=77^{\circ}$.

Step6: Find $m\angle NMP$

Substitute $x=-4$ into the expression for $m\angle NMP$: $m\angle NMP=-20x + 23=-20\times(-4)+23=80 + 23 = 103^{\circ}$.

Answer:

$m\angle LMP = 77^{\circ}$, $m\angle NMP=103^{\circ}$