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

Using the parallel horizontal lines, the line $$AD$$ makes $$112^\circ$$ with the rightward horizontal. Since $$\angle ADF=50^\circ$$, line $$DF$$ makes $$62^\circ$$ with the horizontal, while $$AB$$ makes $$16^\circ$$, so $$x=46^\circ$$. At the other side, the marked $$82^\circ$$ angle and $$\angle CBG=12^\circ$$ give $$y=82^\circ-12^\circ=70^\circ$$. Therefore, $$x+y=46^\circ+70^\circ=116^\circ$$.