Question

construction lupita is building a gate following this diagram. if m∠lmn = 43° and ∠lmn≅∠omp, what is m∠nmp? a 69° b 94° c 137° d 47°

Explanation:

Step1: Identify equal - angle relationship

Since $\angle LMN\cong\angle OMP$ and $m\angle LMN = 43^{\circ}$, then $m\angle OMP=43^{\circ}$.

Step2: Note the straight - angle property

$\angle LMP$ is a straight - angle, so $m\angle LMP = 180^{\circ}$. Also, $\angle LMP=\angle LMN+\angle NMP+\angle OMP$.

Step3: Solve for $m\angle NMP$

We know that $\angle LMN=\angle OMP = 43^{\circ}$ and $\angle LMP = 180^{\circ}$. Substituting into the equation $\angle LMP=\angle LMN+\angle NMP+\angle OMP$, we get $180^{\circ}=43^{\circ}+\angle NMP + 43^{\circ}$. Then $\angle NMP=180^{\circ}-43^{\circ}-43^{\circ}=94^{\circ}$.

Answer:

B. $94^{\circ}$