geometry puzzle

Geometry puzzle (25)

Question
Calculate angel x in picture below.

Solution

Extend AD and BC, intersection is point E.
ΔABE is right angled.
M is center of circle through DBE. ..{see Thales}
M is center of BD.
Now draw perpendicular bisector of BD.
LMCN = 60 - 20 = 40.
LCNM=LDNA=50.
C is on perpendicular bisector of BD.
BC = DC.
x = L CDB = LCBD = 10.