The outer angle of the triangle at the vertex B is three times its inner angle A and 40

The outer angle of the triangle at the vertex B is three times its inner angle A and 40 degrees greater than the inner angle C. Find the angles of the triangle.

The outer and inner corners of the triangle form an unfolded angle of 180 °. Let us denote the inner corner by the letter x and compose the equation:

x + 3x = 180 °;

4x = 180;

x = 180/4 = 45.

Angle B is 45 °. Then the outer angle is B = 180 – 45 = 135 °;

Since it is 40 ° more than the angle С, then the angle С = 135 – 40 = 95 °;

Since the sum of the angles in a triangle is 180 °, we find the angle A:

A = 180 – 95 – 45 = 45 °;