Use the congruence statement to determine that ∠ABF = 5x°. Then, add ∠EBF to ∠FBA to get ∠EBA = 10x°.
Now, remove segment BF and it's easy to see that ∠EBA and ∠CBD are vertical angles, hence equal to each other. This gives you a relationship that lets you find the value of x and the values of all the angles.
... 10x = 2x +84 . . . . vertical angles are equal
... 8x = 84 . . . . . . . . subtract 2x
... x = 10.5 . . . . . . . . . divide by 8
∠EBD is the supplement to ∠CBD, which is 10x° = 105°.
... ∠EBD = 180° -105° = 75°
