Question

Find each measure

Answer 1

in general, when you have an outer angle on the perimeter of a circle, intercepting an arc along the circle (like angle B intercepts arc AC) then the angle is half the arc.

arc ADC is 180 by virtue of being half the whole circle
m<ABC which is an angle on the outer part of the circle, intercepts arc ADC and is thus half the arc ADC from before

arc AB and arc BC make up the other half of the circle, so arc AB + arc BC = 180 and thus x + 3x = 180. solve for x. once you have x, plug it into arc AB = x and arc BC = 3x to get these two measurements.

finally, <A intercepts arc BC so <A is half arc BC
same logic, <C is half arc AB