Question

look at this diagram: if (overline{ij}) and (overline{ln}) are parallel lines and (mangle jkm = 121^{circ}), what is (mangle lmo)?

Explanation:

Step1: Identify angle - relationship

$\angle JLM$ and $\angle LMN$ are same - side interior angles.

Step2: Recall property of parallel lines

For parallel lines $JK$ and $LN$, same - side interior angles are supplementary, i.e., $\angle JLM+\angle LMN = 180^{\circ}$.

Step3: Solve for $\angle LMN$

Given $\angle JLM = 121^{\circ}$, then $\angle LMN=180^{\circ}-\angle JLM$.
$\angle LMN = 180 - 121=59^{\circ}$.

Answer:

$59^{\circ}$