Question

In Quadrilateral ABCD , AB ∥ CD, and m∠2=35°.

Answer 1

Angle 2 and 5 are alternate interior angle and they are congruent. That means that m <5= 35°.

Answer 2

we know that

Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Alternate interior angles are congruent

In this problem

the parallel lines are AB and CD

the transversal line is BD

then

m∠5=m∠2 ------> by alternate interior angles

m∠5=$35\°$

therefore

the answer is

m∠5=$35\°$