Are the angles of ∆ABC and ∆ABD equal in the figure above? Why

Since AC = AD and CB = DB, ∠ACB = ∠ADB.

As both the triangles have AB as a common side, angle between any side and AB in ∆ABC will be a matching angle to angle between

any side and AB in ∆ABD.

So, AC = AD and AB which is common, ∠CAB = ∠CAB.

And, CB = DB and AB which is common, ∠CBA = ∠DBA.

Hence, all the angles of ∆ABC and ∆ABD are equal.