We are asked to find the measure of angle ∠ DBA. Let's find it on the given diagram.
We can see that DA ⊥ AB and DC⊥ CB. We also know that both DA and DC equal 39. Thus, D is equidistant from the sides of ∠ ABC. Now, let's recall the Converse of the Angle Bisector Theorem.
Converse of the Angle Bisector Theorem
If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle.
By this theorem, DB is a bisector of the angle ∠ ABC. Therefore, the measures of the angles ∠ DBA and ∠ DBC are the same. We can conclude that ∠ DBA also measures 17^(∘).
