The total measure of a circle's arc lengths is 360 degrees. We can add up all of the arc lengths of the circle, set it equal to 360, and solve for x. The proportion of arc lengths will be used in that that is how many x's each arc gets.
3x + 5x + 4x = 360
12x = 360
x = 30
Arc AB: 90 degrees
30 x 3 = 90
Arc BC: 150 degrees
30 x 5 = 150
Arc AC: 120 degrees
30 x 4 = 120
Hope this helps!! :)