Question

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

Explanation:

Step1: Identify vertical - angle relationship

$\angle MLN$ and $\angle JIL$ are vertical angles. Since vertical angles are equal, $m\angle JIL=m\angle MLN = 46^{\circ}$.

Step2: Use linear - pair property

$\angle JIL$ and $\angle JIG$ form a linear pair. A linear pair of angles is supplementary, so $m\angle JIL + m\angle JIG=180^{\circ}$.

Step3: Solve for $m\angle JIG$

$m\angle JIG=180^{\circ}-m\angle JIL$. Substitute $m\angle JIL = 46^{\circ}$ into the equation, we get $m\angle JIG=180 - 46=134^{\circ}$.

Answer:

$134$