The outer angle of the triangle is 120 degrees. Find non-adjacent corners with the outer corner

The outer angle of the triangle is 120 degrees. Find non-adjacent corners with the outer corner of the triangle if one of them is 2 times larger than the other.

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 – 120) = 60.

The sum of the interior angles of the triangle is 180, then 180 = (60 + X + 2 * X).

3 * X = 180 – 60 = 120.

X = 120/3 = 40.

Then the angle ABC = 1 * 40 = 40, angle ACB = 2 * 40 = 80.

Answer: Non-adjacent angles are 40 and 80.