Hi Nancy!
For similar triangles the naming matters! So if it says ABD is similar to BCD, it means

Line AB is similar to the line BC;
Line BD is similar to line CD;
Line DA is similar to line DB.

Same for the angles!
So the solution :

Angle ABC = Angle ABD + Angle CBD

But since triangle ABD is similar to triangle BCD.
That means Angle CBD is the same as Angle BAD.

So Angle ABC = Angle ABD + Angle BAD

Angle ABD + Angle BAD = 180° - Angle BCA = 90°
(total internal angles of a triangle = 180°)

So Angle ABC = 90°