The angles all form vertical angles. The ones labeled are vertical to each other and the ones not labeled are vertical to each other. Vertical angles are congruent, therefore, 2x + 50 = 7x. Solving for x you get 50 = 5x and x = 10. That means that that set of vertical angles each have a measure of 70. That's 140 so far. Around the "circle" created by those angles is a total degree measure of 360. So 360 - 140 = 220. Divide that in half to get the measure of angle BED and its vertical angle AEC. So your angle measure, BED is 110.
