Question

1. ∠lmn is a straight angle. find m∠lmp and m∠nmp ( 16x + 13) ( 20x + 23)

Explanation:

Step1: Set up equation

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

$16x+20x+13 + 23=180$, which simplifies to $36x+36 = 180$.

Step3: Solve for x

Subtract 36 from both sides: $36x=180 - 36=144$. Then divide both sides by 36, $x=\frac{144}{36}=4$.

Step4: Find $m\angle{LMP}$

Substitute $x = 4$ into the expression for $m\angle{LMP}$: $m\angle{LMP}=16x+13=16\times4 + 13=64 + 13=69^{\circ}$.

Step5: Find $m\angle{NMP}$

Substitute $x = 4$ into the expression for $m\angle{NMP}$: $m\angle{NMP}=20x+23=20\times4+23=80 + 23=111^{\circ}$.

Answer:

$m\angle{LMP}=69^{\circ}$, $m\angle{NMP}=111^{\circ}$