Question

look at this diagram:
if ( overleftrightarrow{ln} ) and ( overleftrightarrow{oq} ) are parallel lines and ( mangle qpm = 66^circ ), what is ( mangle nmk )?

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. Since \(\angle QPM\) and \(\angle NMK\) are vertical angles.

Step2: Use the property of vertical angles

By the vertical - angles theorem, if two angles are vertical angles, then they are congruent. Given \(m\angle QPM = 66^{\circ}\), and \(\angle QPM\) and \(\angle NMK\) are vertical angles.

Answer:

\(66^{\circ}\)