Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle ghj = 110^{circ}$, what is $mangle fec?$

Explanation:

Step1: Identify vertical - angle relationship

$\angle GHJ$ and $\angle EHI$ are vertical angles. Vertical angles are equal. So $m\angle EHI=m\angle GHJ = 110^{\circ}$.

Step2: Identify corresponding - angle relationship

Since $\overleftrightarrow{DF}$ and $\overleftrightarrow{GI}$ are parallel lines, $\angle FEC$ and $\angle EHI$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So $m\angle FEC=m\angle EHI$.

Answer:

$110$