Question

look at this diagram: if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle nmj = 43^{circ}), what is (mangle nmo?)

Explanation:

Step1: Identify angle - relationship

$\angle NMJ$ and $\angle NMO$ are supplementary angles (linear - pair of angles).

Step2: Use supplementary - angle property

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle NMJ = 43^{\circ}$ and $m\angle NMO=x$. Then $m\angle NMJ + m\angle NMO=180^{\circ}$, so $x + 43^{\circ}=180^{\circ}$.

Step3: Solve for the angle

$x=180^{\circ}-43^{\circ}=137^{\circ}$.

Answer:

$137$