Question

look at this diagram: if (overleftrightarrow{df}) and (overleftrightarrow{gi}) are parallel lines and (mangle ghe = 42^{circ}), what is (mangle feh?)

Explanation:

Step1: Identify angle - relationship

$\angle GHE$ and $\angle FEH$ are alternate - interior angles.

Step2: Apply property of alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So $m\angle FEH=m\angle GHE$.

Answer:

$42$