Question

look at this diagram:
if \\( \overleftrightarrow { d f } \\) and \\( \overleftrightarrow { g i } \\) are parallel lines and \\( m \angle d e h = 67 ^ { \circ } \\), what is \\( m \angle g h e \\)?

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Here, \(\overleftrightarrow{DF}\) and \(\overleftrightarrow{GI}\) are parallel lines and \(JC\) is the transversal. So, \(m\angle DEH+m\angle GHE = 180^{\circ}\).

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

Given \(m\angle DEH = 67^{\circ}\), substitute into the equation \(m\angle GHE=180^{\circ}-m\angle DEH\). Then \(m\angle GHE = 180^{\circ}- 67^{\circ}=113^{\circ}\).

Answer:

\(113\)