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

Step 1: Understand that the sum of the angles in a triangle is always 180 degrees.

Step 2: Given that the ratio of the angles is 5:3:1, add these ratios together. 5 + 3 + 1 = 9.

Step 3: To find the measure of each angle, multiply the total degrees in a triangle (180) by each part of the ratio and then divide by the sum of the ratio (9).

For the first angle (with ratio 5), the calculation is (180 * 5) / 9 = 100 degrees.

For the second angle (with ratio 3), the calculation is (180 * 3) / 9 = 60 degrees.

For the third angle (with ratio 1), the calculation is (180 * 1) / 9 = 20 degrees.

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