Question

look at this diagram: if (overleftrightarrow{bd}) and (overleftrightarrow{eg}) are parallel lines and (mangle dcf = 129^{circ}), what is (mangle gfh?)

Explanation:

Step1: Identify vertical - angle relationship

$\angle DCF$ and $\angle BCH$ are vertical angles, so $m\angle BCH=m\angle DCF = 129^{\circ}$.

Step2: Use corresponding - angle property

Since $\overleftrightarrow{BD}$ and $\overleftrightarrow{EG}$ are parallel, $\angle BCH$ and $\angle GFH$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are congruent. So $m\angle GFH=m\angle BCH$.

Answer:

$129$