Question

look at this diagram: if $overleftrightarrow{hj}$ and $overleftrightarrow{km}$ are parallel lines and $mangle kln = 138^{circ}$, what is $mangle kli$?

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the angles in a linear pair is 180°. $\angle KLN$ and $\angle KLI$ form a linear pair.
Let $m\angle KLI=x$. Then $m\angle KLN + x=180^{\circ}$.

Step2: Substitute the given angle value

We know that $m\angle KLN = 138^{\circ}$. Substituting this value into the equation $138^{\circ}+x = 180^{\circ}$.

Step3: Solve for the unknown angle

To find $x$, we subtract 138° from both sides of the equation: $x=180^{\circ}-138^{\circ}$.
$x = 42^{\circ}$.

Answer:

$42$