Question 386789
I don't know how to insert my own pictures into this solution, so you'll have to bear with me and try to draw the triangle and its angles:


Let angle ABD = BAD = x (since triangle BAD is isosceles). Since angle ABD + angle BAD = angle CDA (since the sum of 2 angles in a triangle is equal to the exterior angle on the third vertex), we can let angle CDA = 2x. Also, since triangle CAD is isosceles, angle ACD is also equal to 2x.


From the diagram, angles ACD and ABD are two of the angles in triangle ABC which add up to 90. Since ACD = 2x and ABD = x, then 2x + x = 90 --> x = angle ABD = 30 degrees.