Question

in quadrilateral abcd, \\(\overline{ab} \parallel \overline{cd}\\) and \\(m\angle 2 = 31^{\circ}\\). what is \\(m\angle 5\\)?

Explanation:

Step1: Identify alternate interior angles

Since $\overline{AB} \parallel \overline{CD}$ and $\overline{BD}$ is a transversal, $\angle 2$ and $\angle 5$ are alternate interior angles.

Step2: Apply alternate interior angles theorem

Alternate interior angles are congruent, so $m\angle 5 = m\angle 2$.

Answer:

31°