In triangle ABC, angle A is 3.5 times greater than angle B, and angle C is 12 ° less than angle A. Find the angles of the triangle.

From the proposed data, it can be seen that the smaller angle in the ABC triangle is the angle B, we will designate it as x. Then the remaining angles of the triangle are obtained: angle A = 3.5x, angle C = (3.5x – 12). Knowing that the sum of the angles of a triangle is 180 °, you can write the equation:
3.5x + x + (3.5x – 12) = 180
8x -12 = 180
8x = 192
x = 24 ° – the value of the angle B;
Angle A = 3.5x = 3.5 * 24 = 84 °;
Angle C = (3.5x – 12) = 3.5 * 24 – 12 = 84 – 12 = 72 °.
Checking: 84 ° + 24 ° + 72 ° = 180 °.
Answer: 84 °, 24 °, 72 ° are the angles of the triangle.