If x is the center of the circle, find angle a . a: 72 b: 78 c: 95 d: 190

Arc EAB is the intercepted arc of angle BCE.  The rule is that the arc is double the angle measure.  So the arc measure totals 102 because 51*2 = 102.  But we already have arc AB as 72, so little tiny arc EA measures 30.  EC is a diameter of the circle because it goes through the center.  That means that arcEABC is a semicircle and semicircles measure 180 degrees.  That means that arc BC measures 180-102 which is 78 degrees.  Angle A intercepts arc DCB.  Arc DC measures 112 and arc BC measures 78 so the whole arc is 112+78 which is 190.  That means that angle A is half of that.  190/2 is 95 degrees.  Choice C.