One of the inner corners of the triangles. It is 2 times larger than the other, and the outer angle at the apex

One of the inner corners of the triangles. It is 2 times larger than the other, and the outer angle at the apex of the third angle is 117 degrees. Find the corners of the triangle.

1. Vertices of the triangle – А, В, С. ∠О = 117 ° – external angle at the vertex С. ∠А is 2 times more than ∠В.

2. By the condition of the problem, A is 2 times greater than ∠B, that is, ∠A = 2∠B.

3. The outer angle of a triangle (∠O), according to its properties, is equal to the total value of two inner angles that are not adjacent to it:

∠О = ∠А + ∠В = 117 °. We replace ∠A with 2∠B in this expression:

2∠В + ∠В = 117 °.

3∠В = 117 °.

∠В = 39 °.

∠А = 2∠В = 2 x 39 ° = 78 °.

∠С = 180 – ∠О = 180 ° – 117 ° = 63 °.

Answer: the angles of the triangle ∠А = 78 °, ∠В = 39 °, ∠С = 63 °.