Question

look at this diagram: if (overleftrightarrow{hj}) and (overleftrightarrow{km}) are parallel lines and (mangle kli = 64^{circ}), what is (mangle jil?)

Explanation:

Step1: Identify angle - relationship

$\angle KLI$ and $\angle JIL$ are alternate - interior angles.

Step2: Apply property of alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overleftrightarrow{HJ}$ and $\overleftrightarrow{KM}$ are parallel and $\angle KLI$ and $\angle JIL$ are alternate - interior angles, $m\angle JIL=m\angle KLI$.

Answer:

$64$