Find the angles of a triangle where the second angle is 17 ° greater than the first and the third

Find the angles of a triangle where the second angle is 17 ° greater than the first and the third angle is 5 ° less than the doubled first angle.

Let’s denote the first angle of the triangle by x °. Let us write down what the other two angles are equal to, according to the condition of the problem:
(x + 17) ° – second angle;
(2x – 5) ° – third angle.
Based on the fact that the sum of the angles in a triangle is 180 °, we can create and solve the equation:
x + (x + 17) + (2x – 5) = 180
x + x + 17 + 2x – 5 = 180
4x = 168
x = 42.
42 ° is the first corner;
x + 17 = 42 + 17 = 59 ° – the second angle;
2x – 5 = 42 * 2 – 5 = 84 – 5 = 79 ° is the third angle.
Let’s check: 42 ° + 59 ° + 79 ° = 180 °
Answer: 42 °, 59 °, 79 ° angles of the triangle.