The formula to use is z = (x+y)/2 where x and y are the measures of the minor arcs (highlighted in blue) and z is the measure of the intersecting chord angles
In this case, x = measure of minor arc DE = 30 y = measure of minor arc AC = unknown z = measure of angle ABC = 90
So, z = (x+y)/2 90 = (30+y)/2 2*90 = 30+y 180 = 30+y y+30 = 180 y = 180-30 y = 150
