Question

bentley wendts p... d.4 transversals of parallel lines: find angle measures
28
look at this diagram:
if \\( \overleftrightarrow { b d } \\) and \\( \overleftrightarrow { e g } \\) are parallel lines and \\( m \angle e f h = 4 7 ^ { \circ } \\), what is \\( m \angle b c f \\)?

Explanation:

Step1: Find the measure of ∠EFC

Since ∠EFH and ∠EFC form a linear - pair (they are adjacent angles on a straight line), and the sum of angles in a linear - pair is \(180^{\circ}\).
If \(m\angle EFH = 47^{\circ}\), then \(m\angle EFC=180^{\circ}-m\angle EFH\)
\(m\angle EFC = 180 - 47=133^{\circ}\)

Step2: Use the property of parallel lines

Because \(\overleftrightarrow{BD}\) and \(\overleftrightarrow{EG}\) are parallel lines and \(HA\) is a transversal.
By the property of alternate interior angles (when two parallel lines are cut by a transversal, alternate interior angles are equal), \(\angle BCF\) and \(\angle EFC\) are alternate interior angles. So \(m\angle BCF=m\angle EFC\)

Answer:

\(133\)