Angles M and K are adjacent. The angle is 24 degrees less than the angle M. Calculate the degree measures of these angles.

Let us denote the value of the angle K through α.

It is known from the problem statement that the angle K is 24 degrees less than the angle M.

Therefore, the angle M is 24 degrees greater than the angle K and the magnitude of the angle M is α + 24 degrees.

Since two adjacent angles make up a flat angle, which is 180 °, we can write the following equation:

α + α + 24 = 180,

solving which, we get:

2α + 24 = 180;

(2α + 24) / 2 = 180/2;

α + 12 = 90;

α = 90 – 12;

α = 78 °.

We find the value of the angle M:

α + 24 = 78 + 24 = 102 °.

Answer: angle K is 78 °, angle M is 102 °.