The problem states that $ABCD$ is a parallelogram. We are given that $m\angle DAB = 32^\circ$ and we need to find $m\angle BCD$.

1. Problem Description

The problem states that $ABCD$ is a parallelogram. We are given that $m\angle DAB = 32^\circ$ and we need to find $m\angle BCD$.

2. Solution Steps

In a parallelogram, opposite angles are congruent. That is,

$m\angle DAB = m\angle BCD$

$m\angle ABC = m\angle CDA$

Since we are given that $m\angle DAB = 32^\circ$, then $m\angle BCD = m\angle DAB = 32^\circ$.

3. Final Answer

$m\angle BCD = 32^\circ$