Points A, B, C located on the circle divide it into three arcs, the degree values of which are 2: 9: 25.

Points A, B, C located on the circle divide it into three arcs, the degree values of which are 2: 9: 25. Find the larger angle of the triangle ABC.

Let the number of degrees in one part be n. Then the sum of all the parts into which the circle is divided should be equal to 360 degrees:

2n + 9n + 25n = 360 °;

36n = 360 °;

n = 10 °.

Arc AB = 2n = 2 * 10 ° = 20 °;

Arc BC = 9n = 9 * 10 ° = 90 °;

Arc CA = 25n = 25 * 10 ° = 250 °.

The sides of the triangle form inscribed angles that are half the degree values of the arcs on which they rest. The largest angle of the triangle is <ACB. It rests on the CA arc:

<ABC = 250 ° / 2 = 125 °.

Answer: <ABC = 125 °.