Points A, B, C, located on a circle, divide it into three arcs, the degree values of which are related as 3:10:11.

Points A, B, C, located on a circle, divide it into three arcs, the degree values of which are related as 3:10:11. Find the degree measure of the smaller of the angles of the triangle ABC.

Let the degree measure of the arc AB = 3 * X0, arc AC = 10 * X0, arc BC = 11 * X0.

Then 3 * X + 10 * X + 11 * X = 360.

X = 360/24 = 150.

Arc AB = 3 * 15 = 45.

AC = 10 * 15 = 150.

BC = 11 * 15 = 165.

The smaller angle is opposite the smaller arc. Then the smaller angle ACB = 45.

Answer: The smallest angle ACB is 45.