The angle A of this triangle is 3 times the angle M, but half less than the angle L. Determine the angles of the triangle.

Let us denote by x the value of the angle A of this triangle.

Let us express in terms of x the values ​​of the other two angles of this triangle.

In the initial data for this task, it is reported that the second angle A is greater than the M angle, but half the angle L.

Consequently, the angle M is three times less than the angle A and is x / 3, and the angle L is twice the angle A and is 2x.

It is known that as a result of the addition of the values ​​of all the angles of any triangle, 180 degrees are always obtained, therefore, the following relation holds:

x + x / 3 + 2x = 180.

We solve this equation:

3x + x / 3 = 180;

10x / 3 = 180;

x / 3 = 180/10;

x / 3 = 18;

x = 18 * 3;

x = 54 °.

Therefore, angle A is 54 °, angle M is 54/3 = 16 °, angle L is 2 * 54 = 108 °.

Answer: angle A is 54 °, angle M is 16 °, angle L is 108 °.