Question

look at this diagram:
if eg and hj are parallel lines and ( mangle gfi = 49.5^{circ} ), what is ( mangle hif )?
( square ).( square^{circ} )

Explanation:

Step1: Use the property of parallel lines

When two parallel lines \(EG\) and \(HJ\) are cut by a transversal \(KD\), \(\angle GFI\) and \(\angle HIF\) are alternate - interior angles.

Step2: Apply the alternate - interior angles theorem

The alternate - interior angles theorem states that if two parallel lines are cut by a transversal, then alternate - interior angles are congruent. So \(m\angle HIF=m\angle GFI\).

Answer:

\(49.5^{\circ}\)