Question

look at this diagram:
if \\( \overleftrightarrow { m o } \\) and \\( \overleftrightarrow { p r } \\) are parallel lines and \\( m \angle p q n = 49 ^ { \circ } \\), what is \\( m \angle o n q \\)?

Explanation:

Step1: Identify the relationship between angles

Since \( \overleftrightarrow{MO} \) and \( \overleftrightarrow{PR} \) are parallel lines and \( LS \) is a transversal. \( \angle PQN \) and \( \angle ONQ \) are alternate - interior angles.

Step2: Use the alternate - interior angles theorem

By the alternate - interior angles theorem, if two parallel lines are cut by a transversal, then alternate - interior angles are congruent. So \( m\angle ONQ=m\angle PQN \).
Given \( m\angle PQN = 49^{\circ} \), then \( m\angle ONQ = 49^{\circ} \).

Answer:

49