Find measure of angle bed a. 10 degrees b. 70 degrees c. 110 degrees d. 170 degrees

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.