Question

look at this diagram! if \\( \overrightarrow { b d } \\) and \\( \overrightarrow { e g } \\) are parallel lines and \\( m \angle g f c = 53 ^ { \circ } \\), what is \\( m \angle e f h \\)?

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. Since \(\angle GFC\) and \(\angle EFD\) are vertical angles, \(m\angle EFD=m\angle GFC = 53^{\circ}\)

Step2: Use linear - pair property

\(\angle EFD\) and \(\angle EFH\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So, \(m\angle EFH=180^{\circ}-m\angle EFD\)
Substitute \(m\angle EFD = 53^{\circ}\) into the formula: \(m\angle EFH=180^{\circ}- 53^{\circ}\)
\(m\angle EFH = 127^{\circ}\)

Answer:

\(127\)