The bisector of section AC intersects section AD at E, and the bisector of section BD intersects section AD at F (ABCD is a convex quadrilateral).
Due to AB=BC=CD, the ABCE and the BCDF quadrilaterals are deltoids, FBC angle is 5x and EBC angle is also 10x/2=5x. E is the same F because both points lie on the segment AD. Hereinafter, the notation E is used.
Then AEB angle = BEC angle = CED angle = 60, hence 7x + 5x = 12x in the ABE triangle = 120. There is x = 10 and in the convex quadrilateral ABCD the angle at C is 360-22x = 140.
The triangles ABE, BEC, and CED are congruent, with angles of 50, 60, and 70, respectively.