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.
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