Question

look at this diagram! if bd and eg are parallel lines and m∠gfh = 130°, what is m∠dcf?

Explanation:

Step1: Identify vertical - angle relationship

$\angle GFH$ and $\angle EFC$ are vertical angles. Since vertical angles are equal, $m\angle EFC=m\angle GFH = 130^{\circ}$.

Step2: Use corresponding - angle property

$\angle EFC$ and $\angle DCF$ are corresponding angles for parallel lines $\overleftrightarrow{BD}$ and $\overleftrightarrow{EG}$ cut by transversal $\overleftrightarrow{AC}$. Corresponding angles of parallel lines are equal. So $m\angle DCF=m\angle EFC$.

Answer:

$130$