Question

look at this diagram:
if \\( \overleftrightarrow { e g } \\) and \\( \overleftrightarrow { h j } \\) are parallel lines and \\( m \angle j i k = 110 ^ { \circ } \\), what is \\( m \angle g f i \\)?

Explanation:

Step1: Find the measure of ∠GIF

Since ∠JIK and ∠GIF are vertical angles, and vertical angles are equal. So \(m\angle GIF = m\angle JIK=110^{\circ}\).

Step2: Use the property of parallel lines

\(\overleftrightarrow{EG}\parallel\overleftrightarrow{HJ}\), and \(DK\) is a transversal. \(\angle GFI\) and \(\angle GIF\) are supplementary angles (consecutive - interior angles). The sum of supplementary angles is \(180^{\circ}\). Let \(x = m\angle GFI\), then \(x+\angle GIF=180^{\circ}\). Substitute \(\angle GIF = 110^{\circ}\) into the equation: \(x + 110^{\circ}=180^{\circ}\). Solve for \(x\): \(x=180^{\circ}- 110^{\circ}\).

Answer:

\(70\)