Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle hik = 140^{circ}$, what is $mangle jik$?

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the measures of two angles that form a linear pair is 180°. $\angle HIK$ and $\angle JIK$ form a linear pair.

Step2: Set up the equation

Let $m\angle JIK=x$. We know that $m\angle HIK + m\angle JIK=180^{\circ}$. Given $m\angle HIK = 140^{\circ}$, the equation is $140^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

Subtract 140° from both sides of the equation: $x=180^{\circ}-140^{\circ}$.
$x = 40^{\circ}$

Answer:

$40$