Question

look at this diagram:
if \\( \overleftrightarrow { qs } \\) and \\( \overleftrightarrow { tv } \\) are parallel lines and \\( m\angle vur = 42 ^ { \circ } \\), what is \\( m\angle qru? \\)

Explanation:

Step1: Identify the relationship between angles

Since \(\overleftrightarrow{QS}\) and \(\overleftrightarrow{TV}\) are parallel lines, \(\angle VUR\) and \(\angle QRU\) are alternate - interior angles.

Step2: Use the alternate - interior angles theorem

The alternate - interior angles theorem states that if two parallel lines are cut by a transversal, then alternate - interior angles are congruent. So \(m\angle QRU=m\angle VUR\).

Answer:

\(42\)