Question

look at this diagram:
if \\( \overleftrightarrow { e g } \\) and \\( \overleftrightarrow { h j } \\) are parallel lines and \\( m \angle h i k = 115 ^ { \circ } \\), what is \\( m \angle j i k \\)?

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\).
So, \(m\angle HIK + m\angle JIK=180^{\circ}\)

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

Given \(m\angle HIK = 115^{\circ}\), then \(m\angle JIK=180^{\circ}-m\angle HIK\)
Substitute \(m\angle HIK = 115^{\circ}\) into the equation: \(m\angle JIK = 180^{\circ}- 115^{\circ}\)
\(m\angle JIK=65^{\circ}\)

Answer:

\(65\)