Question

bentley wendts p... d.4 transversals of parallel lines: find angle measures
look at this diagram:
if \\( \overleftrightarrow { b d } \\) and \\( \overleftrightarrow { e g } \\) are parallel lines and \\( m \angle b c f = 63 ^ { \circ } \\), what is \\( m \angle g f c? \\)

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines (\(\overleftrightarrow{BD}\) and \(\overleftrightarrow{EG}\)) are cut by a transversal (\(\overleftrightarrow{HA}\)), the sum of the interior angles on the same side of the transversal is \(180^{\circ}\).
So, \(m\angle BCF + m\angle GFC=180^{\circ}\)

Step2: Solve for \(m\angle GFC\)

Given \(m\angle BCF = 63^{\circ}\), substitute into the equation:
\(m\angle GFC=180^{\circ}-m\angle BCF\)
\(m\angle GFC = 180^{\circ}- 63^{\circ}\)
\(m\angle GFC=117^{\circ}\)

Answer:

\(117\)