Question

look at this diagram:
if \\( \overleftrightarrow { d f } \\) and \\( \overleftrightarrow { g i } \\) are parallel lines and \\( m \angle f e h = 125 ^ { \circ } \\), what is \\( m \angle g h e \\)?

Explanation:

Step1: Use the property of adjacent angles on a straight line

Adjacent angles on a straight line sum to \(180^{\circ}\). Let \(m\angle GHE = x\). Since \(\angle FEH\) and \(\angle GHE\) are adjacent angles on a straight - line (because \(DF\parallel GI\) and \(JC\) is a transversal, and they form a linear pair), we have the equation \(x + m\angle FEH=180^{\circ}\).

Step2: Substitute the value of \(m\angle FEH\) into the equation

Given \(m\angle FEH = 125^{\circ}\), substitute it into the equation \(x + 125^{\circ}=180^{\circ}\).
Then solve for \(x\): \(x=180^{\circ}- 125^{\circ}\).

Answer:

\(55\)