the sum of the interior angles of a circle must add up to 360 degrees.
thats how you determined the angles of SR was 100 degrees
360 degrees is equivalent to the total circumference
90 degrees is equivalent to 1/4 of the total circumference (90/360 = 1/4)
hence, if 80/360 is equal to 12, then you could use proportions in order to determine what the corresponding length of SR is
80/360 =12 ---> 80/ (360 *12) =1
100/360 = x ---> 100/(360 *x )=1
so 80/(360*12) = 100/(360x)
doing some rearranging and canceling
x/100 = 12/80
solve for x