Question

lupita is building a gate following this diagram.
if ( mangle lmn = 43^{circ} ) and ( angle lmncongangle omp ), what is ( mangle nmp )?
( mangle nmp=)

Explanation:

Step1: Use the property of a straight - line angle

A straight - line angle measures \(180^{\circ}\). In the diagram, \(\angle LMN+\angle NMP+\angle OMP = 180^{\circ}\) (since \(L, M, O\) are colinear).

Step2: Substitute the given values

Given that \(m\angle LMN = 43^{\circ}\) and \(\angle LMN\cong\angle OMP\), so \(m\angle OMP=43^{\circ}\).
Substitute into the equation \(\angle LMN+\angle NMP+\angle OMP = 180^{\circ}\):
\(43^{\circ}+\angle NMP + 43^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle NMP\)

Combine like terms: \(\angle NMP+86^{\circ}=180^{\circ}\).
Subtract \(86^{\circ}\) from both sides: \(\angle NMP=180^{\circ}- 86^{\circ}\).

Answer:

\(94\)