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

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.

1. Let X be the smallest angle of the triangle.

The average angle is known to be 18 degrees greater.

Then its size is (X + 18).

The largest angle is 24 degrees greater than the average angle.

So it is equal to (X + 18 + 24) = (X + 42).

2. The sum of the angles of a triangle is always 180 degrees

X + X + 18 + X + 42 = 180.

3 * X + 60 = 180.

3 * X = 180 – 60.

3 * X = 120.

X = 120/3.

X = 40 degrees is the smallest angle of the triangle.

X + 42 = 40 + 42 = 82 degrees is the largest angle.

Answer: 82 degrees is the largest angle