Question

look at this diagram: if (overleftrightarrow{jl}) and (overleftrightarrow{mo}) are parallel lines and (mangle mnk = 111^{circ}), what is (mangle lkn?)

Explanation:

Step1: Identify angle - relationship

$\angle MNK$ and $\angle LKN$ are supplementary angles since $\overleftrightarrow{JL}$ and $\overleftrightarrow{MO}$ are parallel lines and $\overleftrightarrow{IP}$ is a transversal.

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle LKN=x$. Then $m\angle MNK + x=180^{\circ}$. Given $m\angle MNK = 111^{\circ}$, we have $x = 180^{\circ}-111^{\circ}$.

Step3: Calculate the angle measure

$x=180 - 111=69^{\circ}$

Answer:

$69$