The outer corner of the triangle is 75 °. The values of the angles not adjacent to it are 1: 2.

The outer corner of the triangle is 75 °. The values of the angles not adjacent to it are 1: 2. Find the degree measures of the angles of the triangle.

Let the value of the angle ABC be equal to X0, then, by condition, the angle ACB is equal to 2 * X0.

The angles DAB and BAC are adjacent, the sum of which is 180, then the angle BAC = (180 – 75) = 105.

The sum of the interior angles of the triangle is 180, then 180 = (105 + X + 2 * X).

3 * X = 180 – 105 = 75.

X = 75/3 = 25.

Then the angle ABC = 1 * 25 = 25, the angle ACB = 2 * 25 = 50.

Answer: The angles of the triangle are 25, 50, 105.