Question

look at this diagram: if $overleftrightarrow{jl}$ and $overleftrightarrow{mo}$ are parallel lines and $mangle{jki}=115^{circ}$, what is $mangle{lkn}$?

Explanation:

Step1: Identify angle - relationship

$\angle{JKI}$ and $\angle{KNO}$ are corresponding angles. Since $\overleftrightarrow{JL}$ and $\overleftrightarrow{MO}$ are parallel, $m\angle{KNO}=m\angle{JKI} = 115^{\circ}$ (corresponding - angles postulate).

Step2: Use linear - pair property

$\angle{KNO}$ and $\angle{LKN}$ form a linear pair. The sum of the measures of angles in a linear pair is $180^{\circ}$. Let $x = m\angle{LKN}$. Then $x + 115^{\circ}=180^{\circ}$.

Step3: Solve for the angle measure

$x=180^{\circ}- 115^{\circ}=65^{\circ}$.

Answer:

$65^{\circ}$