Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle hik = 46^{circ}$, what is $mangle jik?$

Explanation:

Step1: Recall angle - addition property

Angles $\angle HIK$ and $\angle JIK$ form a linear - pair. A linear - pair of angles are supplementary, meaning their sum is $180^{\circ}$.
So, $\angle HIK+\angle JIK = 180^{\circ}$.

Step2: Solve for $\angle JIK$

We know that $\angle HIK = 46^{\circ}$. Let $x=\angle JIK$. Then $46^{\circ}+x = 180^{\circ}$.
Subtract $46^{\circ}$ from both sides: $x=180^{\circ}-46^{\circ}$.
$x = 134^{\circ}$.

Answer:

$134$