Answer
$m \angle ABD$ < $m \angle CBD$
Work Step by Step
According to the Converse of the Hinge Theorem, if two consecutive sides in a triangle are congruent to two consecutive sides in another triangle, but their third sides are not congruent, then the included angle that is opposite the longer side is the larger angle of the included angles in both triangles.
Two sides in one triangle are congruent to two consecutive sides in another triangle. $\overline{AB}$ is marked congruent to $\overline{CB}$. $\overline{BD}$ is congruent to $\overline{BD}$ because they are shared by both triangles.
$AD$ in $\triangle ABD$ is $8$ whereas $CD$ in $\triangle CBD$ is $10$; therefore, $CD$ is the longer side, and the angle opposite to it will be the larger angle.
$m \angle ABD$ < $m \angle CBD$
