Question

look at this diagram: if \\( \overleftrightarrow { h j } \\) and \\( \overleftrightarrow { k m } \\) are parallel lines and \\( m \angle m l n = 125 ^ { \circ } \\), what is \\( m \angle k l n \\)?

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\). Let \(m\angle KLN = x\). We know that \(\angle MLN+x = 180^{\circ}\) (since \(\overrightarrow{KM}\) is a straight - line segment and \(\angle MLN\) and \(\angle KLN\) are adjacent angles).

Step2: Solve for \(x\)

Given \(m\angle MLN=125^{\circ}\), substitute into the equation \(\angle MLN + x=180^{\circ}\). Then \(x = 180^{\circ}-\angle MLN\).
Substitute \(\angle MLN = 125^{\circ}\) into the formula: \(x=180 - 125\).

Answer:

\(55\)