In Square ABCD all sides are equal =d

In Equilateral Triangle BEC all sides are equal =d

ABCD is a square and BCE is an equilateral triangle.

The angle DCE = 90 + 60 or 150 degrees.

Since BCE is an equilateral triangle, CE = CB = CD, so DEC is an isosceles triangle.

So angle DEC = angle EDC = x degrees

So x+x+150=180

x = (180 - 150)/2 = 30/2 = 15 degrees.

**Option A is the Correct Answer.**