CIRCLES-cyclic Quadrilaterals

Let ABCD be a cylclic quadrilateral.  AEB, BFC, CGD and DHA are in respective segments.
               of AB, BC, CD and DA.

 Join the  diagonal AC.
              H + ACD = 180  ........(i)   (opp. angles of a cyclic quad.)
               E +  ACB = 180 .........(ii)
               F + BAC = 180  ........(iii)
                G + CAD = 180  ........(iv)
               adding (i), (ii), (iii) and (iv) gives us the solution