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 - angled relationship

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

Step2: Note that $\angle NMP$ and $\angle LMN+\angle OMP$ are supplementary

The sum of angles $\angle LMN$, $\angle OMP$ and $\angle NMP$ is $180^{\circ}$ (a straight - angle). Let $x = m\angle NMP$. Then $x+43^{\circ}+43^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle NMP$

$x=180^{\circ}-(43^{\circ}+43^{\circ})=180^{\circ}-86^{\circ}=94^{\circ}$.

Answer:

B. $94^{\circ}$