Question

look at this diagram:
if \\( \overleftrightarrow { d f } \\) and \\( \overleftrightarrow { g i } \\) are parallel lines and \\( m \angle i h e = 138 ^ { \circ } \\), what is \\( m \angle f e h? \\)

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Here, \(DF\parallel GI\) and \(CJ\) is the transversal. \(\angle IHE\) and \(\angle FEH\) are consecutive interior angles.
The formula for supplementary angles is \(m\angle IHE + m\angle FEH=180^{\circ}\)

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

Given \(m\angle IHE = 138^{\circ}\), substitute into the formula:
\(m\angle FEH=180^{\circ}-m\angle IHE\)
\(m\angle FEH = 180^{\circ}- 138^{\circ}\)
\(m\angle FEH=42^{\circ}\)

Answer:

\(42\)