The first angle in the triangle is 25 ° more than the second, and the second is 2 times more than the third.

The first angle in the triangle is 25 ° more than the second, and the second is 2 times more than the third. Find the value of the first angle of this triangle if the sum of its second and third angles is 120 °.

Three angles α1, α2, α3 are given.

The system of equations compiled according to the condition:

(1) α1 = α2 + 25º,

(2) α2 = 2 * α3,

(3) α2 + α3 = 120º.

And it is known that α1 + α2 + α3 = 180º (4).

Substitute the value of the angle α1 in the fourth equation.

Then, α2 + 25º + 120º = 180º.

α2 = 180º – 145º = 35º.

Therefore, α1 = 35º + 25º = 60º.

Note: in this problem, the first and second conditions are superfluous, since it is seen from (3) and (4) conditions that the angle α1 = 60º.

Answer: the first angle is 60º.