Question

look at this diagram:
if \\( \overleftrightarrow { f h } \\) and \\( \overleftrightarrow { i k } \\) are parallel lines and \\( m \angle f g e = 69 ^ { \circ } \\), what is \\( m \angle f g j \\)?

Explanation:

Step1: Identify the relationship between angles

Since \( \overleftrightarrow{FH} \) and \( \overleftrightarrow{IK} \) are parallel lines and \( EL \) is a transversal. \( \angle FGE \) and \( \angle FGJ \) are supplementary angles (they form a linear - pair).

Step2: Use the supplementary - angle formula

The sum of supplementary angles is \( 180^{\circ} \). If \( m\angle FGE = 69^{\circ} \), and \( m\angle FGE+m\angle FGJ = 180^{\circ} \), then \( m\angle FGJ=180^{\circ}-m\angle FGE \).
Substitute \( m\angle FGE = 69^{\circ} \) into the formula: \( m\angle FGJ = 180 - 69\).

Answer:

\(111\)