The outer angle of the triangle at the vertex B is 3 times its inner angle A and 40 ° greater than the inner angle C. Find all the angles.

1. Draw an arbitrary triangle ABC, then extend side AB to an arbitrary ray AD. Angle СBD – external angle of triangle ABC. 2. The sum of the angles СBD ​​and СВА is equal to 180 degrees, as the adjacent angles for straight line AD and secant BC, then let the angle А be equal to x, then the angle СBD is equal to (3 * x), therefore the angle СВА is equal to (180 – (3 * x) ), and the angle C is equal to ((3 * x) – 40). The sum of the angles of a triangle is 180 degrees, let’s make the equation:

x + (180 – (3 * x)) + ((3 * x) – 40) = 180, open the brackets, we get:

x = 40, therefore, angle A is 40, angle CBA is 60, angle C is 80, angle CBD is 120.

Answer: angle A is 40, angle CBA is 60, angle C is 80, angle CBD is 120.