Question

in quadrilateral abcd, \\( \overline { a b } \parallel \overline { c d } \\) and \\( m \angle 2 = 35 ^ { \circ } \\). what is \\( m \angle 5 \\)? enter your answer in the box.

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

The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the alternate interior angles are congruent. So, \( m\angle 5 = m\angle 2 \).

Step3: Substitute the Given Value

We know \( m\angle 2 = 35^\circ \), so \( m\angle 5 = 35^\circ \).

Answer:

\( 35 \)