In the adjoining figure $$\angle DCE = 10^\circ$$, $$\angle CED = 98^\circ$$, $$\angle BDF = 28^\circ$$.

Then the measure of angle $$x$$ is

In $$\triangle CDE$$

$$\angle CDE = 180\degree - \angle DCE -\angle CED =180\degree - 10\degree - 98\degree = 72\degree$$

Since ABCD is a cyclic quadrilateral 

$$\angle BAD + \angle BCD = 180\degree $$ 

$$\angle FAB = \angle FDB =28\degree$$ (Angles subtended by the same chord at different points on the circle)

Now, in quadrilateral GACE,

$$x + \angle FAB + \angle BAD + \angle BCD + \angle DCE+ \angle DEC =360\degree$$ (Angle sum property)

$$ x = 360\degree- (28\degree+ 180\degree+10\degree + 98\degree ) =44\degree$$