In the adjoining figure, $$\angle BAE=16^\circ$$ and $$\angle CBG=12^\circ$$. Then the measure of $$x+y$$ in degrees is

$$\angle FDG = 180\degree - (68\degree + 50\degree) = 62\degree$$ (Straight angle)

AE || DC, 

$$ \angle FIE = \angle FDG = 62\degree$$ (Corresponding angles)

In $$\triangle KIA$$

$$\angle KIA = 180\degree- 62\degree = 118\degree$$

$$\angle AKI = 180\degree - (16\degree + 118\degree) = 46\degree$$

Now $$ x = \angle AKI = 46\degree$$ ( Vertically opposite angles)

Similarly,

$$\angle BLE = 82 \degree$$ (corresponding angles)

$$ \angle BLJ = 180\degree - \angle BLE = 98\degree $$(Straight angle)

$$ \angle BJL = 180\degree - 98\degree - 12\degree = 70\degree$$( Angle sum property of triangle)

$$ y = \angle BJL = 70\degree$$ (Vertically opposite angles)

Thus,

$$x+y = 116\degree$$