Question

look at this diagram:
if (overleftrightarrow{hj}) and (overleftrightarrow{km}) are parallel lines and (mangle mli = 119^{circ}), what is (mangle kln)?

Explanation:

Step1: Find the measure of adjacent angle

Since $\angle MLI$ and $\angle KLM$ form a linear - pair (they are adjacent and supplementary), and $m\angle MLI = 119^{\circ}$.
We know that $\angle MLI+\angle KLM = 180^{\circ}$.
So, $\angle KLM=180^{\circ}-\angle MLI$.
Substitute $\angle MLI = 119^{\circ}$ into the formula: $\angle KLM = 180^{\circ}-119^{\circ}=61^{\circ}$.

Step2: Use the property of vertical angles

$\angle KLN$ and $\angle KLM$ are vertical angles.
By the vertical - angles theorem (vertical angles are equal), $m\angle KLN=m\angle KLM$.

Answer:

$61$