Beam AB divided the angle MAK into two angles MAB and BAK. The degree measure of the angle BAK is 3/7 of the angle MAB.

Beam AB divided the angle MAK into two angles MAB and BAK. The degree measure of the angle BAK is 3/7 of the angle MAB. The angle BAK is 24 degrees less than the angle MAB. Find the angle measure MAK.

Let’s denote the degree measure of the angle MAB as xo. Since, in accordance with the condition of the given specification, the angle BAK is 3/7 of the angle MAB, and the difference between the angles is 24o, then the following equation can be drawn up:

x – 3/7 * x = 24.

Now let’s simplify the left side of the equation and find out what x is:

x – 3/7 * x = 24;

4/7 * x = 24 | * 7/4;

x = 42o.

This means that the MAB angle is 42o. Then the angle BAK is equal to:

BAK = 42 – 24 = 18.

Then the angle MAK is equal to:

MAK = MAB + BAK = 42 + 24 = 66.

Answer: MAK = 66.