To find \( m \angle NOL \), we start by noting the relationships between the angles based on the given information about the parallel lines \( KM \) and \( NP \).
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Understanding the Diagram: Since \( KM \) and \( NP \) are parallel lines, any transversal that intersects them will create corresponding angles and alternate interior angles.
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Identifying the Angles: We know \( m \angle MLO = 136^\circ \). Since \( KM \) and \( NP \) are parallel and \( LO \) is a transversal that intersects these parallel lines, angles \( MLO \) and \( NOL \) are on opposite sides of the transversal.
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Using Alternate Interior Angles: \( m \angle MLO \) and \( m \angle NOL \) are alternate interior angles, which means they are equal in measurement when two parallel lines are cut by a transversal.
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Calculating \( m \angle NOL \): \[ m \angle NOL = m \angle MLO = 136^\circ. \]
Therefore, the measure of angle \( NOL \) is \( \boxed{136^\circ} \).