The degree measures of the angles of the triangle are proportional to the numbers 2,5,8.

The degree measures of the angles of the triangle are proportional to the numbers 2,5,8. find the degree measure of the smaller angle.

Let one of the angles be equal to 2 * X, then the second angle will be 5 * X, and the third angle will be 8 * X.

The sum of the angles of a triangle is 180, then:

2 * X + 5 * X + 8 * X = 180.

15 * X = 180.

X = 180/15 = 12.

Then the first angle is 2 * 12 = 240.

The second angle is 5 * 12 = 60.

The third angle is 8 * 12 = 96.

Answer: The degree measure of the smaller angle is 24.