Find the degree measures of the angles of the triangle MNK if the angle M is less than the angle N

Find the degree measures of the angles of the triangle MNK if the angle M is less than the angle N by 40 ° and more than the angle K by 10 °. 

Let the angle M be equal to x, then the angle N – x + 40 °, the angle K – x – 10 °.

The sum of all the angles of a triangle is 180 °. Thus,

x + x + 40 + x – 10 = 180;

3x = 150;

x = 50 ° is the degree measure of the angle M.

This means that the degree measure of the angle N is 90 °, and the angle K is 40 °.