To find m∠ ABD, let's first consider ∠ ABC. We can see that CD and DA connect the point D with the sides of ∠ ABC. Moreover, they are congruent and perpendicular to the sides.
According to the Converse of the Angle Bisector Theorem, if a point is in the interior of an angle and is equidistant from its two sides, then it lies on the bisector of the angle. This means that BD forms a bisector of ∠ ABC.
Since an angle bisector divides an angle into two congruent adjacent angles, ∠ DBC≅ ∠ ABD. Therefore, m∠ ABD=20^(∘).
