Question

look at this diagram: if (overrightarrow{fh}) and (overrightarrow{ik}) are parallel lines and (mangle jig = 137^{circ}), what is (mangle hgi?)

Explanation:

Step1: Identify angle - relationship

$\angle JIG$ and $\angle HGI$ are same - side interior angles.

Step2: Recall property of same - side interior angles

Same - side interior angles of parallel lines are supplementary, i.e., their sum is $180^{\circ}$.
Let $m\angle HGI = x$. We know that $m\angle JIG=137^{\circ}$ and $m\angle JIG + x=180^{\circ}$.

Step3: Solve for $x$

$x = 180^{\circ}-m\angle JIG$.
Substitute $m\angle JIG = 137^{\circ}$ into the equation: $x=180 - 137=43^{\circ}$.

Answer:

$43$