On a circle with center O, points A and B are marked so that ∠AOB = 40 °. The length of the smaller arc AB is 50. Find the length of the larger arc

∠AOB – is central and is equal to the degree measure of the arc on which it relies.
Therefore, the degree measure of the smaller arc AB is also 40 °.
So the degree measure of the larger arc is 360 ° -40 ° = 320 °
Let x be the length of the larger arc, then we get the proportion:
40 ° – length 50
320 ° – length x
40/320 = 50 / x
x = 320 * 50/40 = 8 * 50 = 400
Answer: 400