Remark
Nice application problem. Thanks for posting. The angle x = 1/2 the positive difference between the two intersected arcs.
Givens
largest arc = x + 60
Smallest arc = 20
intersection angle between the two secants = x
Solution
x = (x + 60 - 20)/2 Multiply both sides by 2
2x = (x + 40) Subtract x from both sides
x = 40
