Question

look at this diagram:
if \\( \overleftrightarrow { l n } \\) and \\( \overleftrightarrow { o q } \\) are parallel lines and \\( m \angle l m p = 115 ^ { \circ } \\), what is \\( m \angle o p m \\)?

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Here, \(LN\parallel OQ\) and \(RK\) is the transversal. \(\angle LMP\) and \(\angle OPM\) are consecutive interior angles.
The formula for supplementary angles is \(m\angle LMP + m\angle OPM=180^{\circ}\)

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

Given \(m\angle LMP = 115^{\circ}\), substitute into the formula:
\(m\angle OPM=180^{\circ}-m\angle LMP\)
\(m\angle OPM = 180^{\circ}- 115^{\circ}\)
\(m\angle OPM=65^{\circ}\)

Answer:

\(65\)