Question

look at this diagram:
if (overleftrightarrow{bd}) and (overleftrightarrow{eg}) are parallel lines and (mangle bca = 113^{circ}), what is (mangle dcf)?

Explanation:

Step1: Recognize vertical angles

Vertical angles are equal. $\angle BCA$ and $\angle DCF$ are vertical angles.

Step2: Use the property of vertical angles

Since $\angle BCA = 113^{\circ}$ and $\angle BCA=\angle DCF$ (vertical angles), then $m\angle DCF = 113^{\circ}$.

Answer:

$113$