Question

look at this diagram: if $overleftrightarrow{km}$ and $overleftrightarrow{np}$ are parallel lines and $mangle poq = 53^circ$, what is $mangle nol$?

Explanation:

Step1: Identify Alternate Interior Angles

Since \( \overleftrightarrow{KM} \parallel \overleftrightarrow{NP} \) and \( \overleftrightarrow{JQ} \) is a transversal, \( \angle POQ \) and \( \angle NOL \) are alternate interior angles.

Step2: Apply Alternate Interior Angles Theorem

Alternate interior angles are congruent when two parallel lines are cut by a transversal. So \( m\angle NOL = m\angle POQ \).

Step3: Substitute the Given Angle Measure

Given \( m\angle POQ = 53^\circ \), thus \( m\angle NOL = 53^\circ \).

Answer:

\( 53 \)