Question

if (overleftrightarrow{bd}) and (overleftrightarrow{eg}) are parallel lines and (mangle efh = 43^{circ}), what is (mangle gfh?)

Explanation:

Step1: Recall angle - sum property

$\angle EFH$ and $\angle GFH$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So, $m\angle EFH + m\angle GFH=180^{\circ}$.

Step2: Solve for $m\angle GFH$

We know that $m\angle EFH = 43^{\circ}$. Substitute this value into the equation $m\angle EFH + m\angle GFH = 180^{\circ}$. Then $m\angle GFH=180^{\circ}-m\angle EFH$.
$m\angle GFH = 180 - 43=137^{\circ}$

Answer:

$137$