Question

look at this diagram: if $overleftrightarrow{jl}$ and $overleftrightarrow{mo}$ are parallel lines and $mangle lkn = 40^{circ}$, what is $mangle lki$?

Explanation:

Step1: Identify angle - relationship

$\angle LKN$ and $\angle LKI$ are supplementary angles (a linear - pair of angles).

Step2: Recall the property of supplementary angles

The sum of two supplementary angles is $180^{\circ}$. So, $m\angle LKN + m\angle LKI=180^{\circ}$.

Step3: Solve for $m\angle LKI$

Given $m\angle LKN = 40^{\circ}$, then $m\angle LKI=180^{\circ}-m\angle LKN$. Substitute $m\angle LKN = 40^{\circ}$ into the equation: $m\angle LKI = 180 - 40=140^{\circ}$.

Answer:

$140$