Question

look at this diagram: if \\( \overleftrightarrow { d f } \\) and \\( \overleftrightarrow { g i } \\) are parallel lines and \\( m \angle i h j = 46 ^ { \circ } \\), what is \\( m \angle f e h \\)?

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. Since \(\angle IHJ\) and \(\angle EHG\) are vertical angles, \(m\angle EHG = m\angle IHJ=46^{\circ}\).

Step2: Use the property of parallel lines (corresponding angles)

\(\overleftrightarrow{DF}\parallel\overleftrightarrow{GI}\), and \(CJ\) is a transversal. \(\angle FEH\) and \(\angle EHG\) are alternate - interior angles. For parallel lines \(DF\) and \(GI\) with transversal \(CJ\), \(m\angle FEH=m\angle EHG\).

Answer:

\(46\)