What is the largest of the angles of a triangle if the difference between it and the average angle is 24

What is the largest of the angles of a triangle if the difference between it and the average angle is 24 degrees, and between the average and the smallest angle is -18 degrees?

Let x be the average angle, then the larger angle is x + 24, and the smaller x is 18. The sum of the angles in the triangle x + x + 24 + x is 18 or 180. Solve for x:

x + x + 24 + x – 18 = 180;

3 * x = 180 – 6;

3 * x = 174;

x = 58.

By condition, a larger angle is needed, which means 58 + 24 = 82.

Answer: 82.