Question

look at this diagram:
if (overleftrightarrow{eg}) and (overleftrightarrow{hj}) are parallel lines and (mangle gfi = 117^{circ}), what is (mangle hif)?
(square^{circ})

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(EG\) and \(HJ\) are cut by a transversal \(DK\), \(\angle GFI\) and \(\angle HIF\) are consecutive interior angles.
The sum of consecutive interior angles is \(180^{\circ}\).
So, \(m\angle GFI + m\angle HIF=180^{\circ}\)

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

Given \(m\angle GFI = 117^{\circ}\), substitute into the equation:
\(m\angle HIF=180^{\circ}-m\angle GFI\)
\(m\angle HIF = 180^{\circ}- 117^{\circ}\)
\(m\angle HIF=63^{\circ}\)

Answer:

\(63\)