# 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

May 31, 2020 | Education

| ∠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

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