The measure of three angles of a triangle are in the ratio 5 : 3 : 1. Find the measures of these angles.

Sure, here are the steps to find the measures of the angles:

1. We know that the sum of the angles in a triangle is 180 degrees.

2. The problem states that the measures of the angles are in the ratio 5:3:1. If we add these ratios together, we get 5 + 3 + 1 = 9.

3. To find the measure of each angle, we divide the total degrees in a triangle (180) by the sum of the ratios (9). So, 180 ÷ 9 = 20 degrees. This is the measure of the smallest angle (the one with the ratio of 1).

4. To find the measures of the other two angles, we multiply this number by their respective ratios. So, for the angle with the ratio of 3, we do 20 x 3 = 60 degrees. For the angle with the ratio of 5, we do 20 x 5 = 100 degrees.

So, the measures of the three angles are 100 degrees, 60 degrees, and 20 degrees.