Question

look at this diagram: if (overrightarrow{df}) and (overrightarrow{gi}) are parallel lines and (mangle dec = 52^{circ}), what is (mangle ghj?)

Explanation:

Step1: Identify angle - type relationship

$\angle DEC$ and $\angle GHJ$ are corresponding angles.

Step2: Apply corresponding - angles property

When two parallel lines are cut by a transversal, corresponding angles are congruent. Since $\overleftrightarrow{DF}\parallel\overleftrightarrow{GI}$ and $\angle DEC$ and $\angle GHJ$ are corresponding angles, $m\angle GHJ=m\angle DEC$.

Answer:

$52$