The angle M of the triangle MNK is 2 times less than the angle N and 3 times less than the angle K.

The angle M of the triangle MNK is 2 times less than the angle N and 3 times less than the angle K. Find all the angles of the triangle MNK.

Let’s solve this problem using the equation.

Let the degree measure of the angle M be equal to x degrees, then the degree measure of the angle N is 2 * x degrees, and the degree measure of the angle K is 3 * x degrees. We know that the sum of the degree measures of a triangle is 180 degrees. Let’s make the equation:

x + 2 * x + 3 * x = 180;

x * (1 + 2 + 3) = 180;

x * 6 = 180;

x = 180: 6;

x = 30 degrees – the degree measure of the angle M;

2 * 30 = 60 degrees – the degree measure of the angle N;

3 * 30 = 90 degrees – the degree measure of the angle K.

Answer: 60 degrees; 30 degrees; 90 degrees.