Question

in the figure jklm, $overleftrightarrow{kl}paralleloverleftrightarrow{jm}$ and $overleftrightarrow{jk}paralleloverleftrightarrow{ml}$. what is the value of $angle kjl$?

Explanation:

Step1: Find the alternate - interior angle

Since $KL\parallel JM$, the alternate - interior angle to the $125^{\circ}$ angle at point $K$ is also $125^{\circ}$ at point $J$. Let's call this angle $\angle KJM$.

Step2: Calculate $\angle KJL$

We know that $\angle KJM$ is composed of $\angle KJL$ and the $20^{\circ}$ angle. So, $\angle KJL=\angle KJM - 20^{\circ}$. Substituting the value of $\angle KJM = 125^{\circ}$, we get $\angle KJL=125^{\circ}- 20^{\circ}$.
$125 - 20=105^{\circ}$ is wrong. We should use the fact that the angle adjacent to the $125^{\circ}$ angle at $K$ and $\angle KJL$ and the $20^{\circ}$ angle are related. The angle adjacent to the $125^{\circ}$ angle at $K$ is $180 - 125=55^{\circ}$ (linear - pair). Since $KL\parallel JM$, this $55^{\circ}$ angle and $\angle KJL$ and the $20^{\circ}$ angle are related. $\angle KJL=55^{\circ}-20^{\circ}$.
$55 - 20 = 35^{\circ}$

Answer:

F. $35^{\circ}$