Question

look at this diagram: if (overleftrightarrow{jl}) and (overleftrightarrow{mo}) are parallel lines and (mangle lki = 126^{circ}), what is (mangle onk?)

Explanation:

Step1: Identify vertical - angle relationship

$\angle LKI$ and $\angle JKN$ are vertical angles. Vertical angles are equal. So $m\angle JKN=m\angle LKI = 126^{\circ}$.

Step2: Identify corresponding - angle relationship

Since $\overleftrightarrow{JL}$ and $\overleftrightarrow{MO}$ are parallel lines, $\angle JKN$ and $\angle ONK$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So $m\angle ONK=m\angle JKN$.

Answer:

$126$