Question

look at this diagram: if $overleftrightarrow{ce}$ and $overleftrightarrow{fh}$ are parallel lines and $mangle fgd = 43^{circ}$, what is $mangle edg$?

Explanation:

Step1: Recall angle - relationship

When two parallel lines are cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary. $\angle FGD$ and $\angle EDG$ are supplementary because they are same - side interior angles.

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle FGD = 43^{\circ}$ and $m\angle EDG=x$. Then $m\angle FGD + m\angle EDG=180^{\circ}$, so $x + 43^{\circ}=180^{\circ}$.

Step3: Solve for the angle

Subtract $43^{\circ}$ from both sides of the equation: $x=180^{\circ}-43^{\circ}=137^{\circ}$.

Answer:

$137$