The ratio of the measures of the angles of a triangle is 3:8:9. Find the measure of each angle.

Question

Ratios & Proportions

Answer 1

3x + 8x + 9x = 180

20x = 180

x = 180/20

x = 9⁰

3x = 3(9) = 27⁰ Is the smallest angle

8x = 8(9). = 72⁰ is the second angle

9x = 9(9) = 81⁰ is the largest angle

To check: 27 + 72 + 81 = 180

Answer 2

The ratio of 3:8:9 can be represented as angle measurements of 3x, 8x and 9x. That means that 3x + 8x + 9x = 20x = 180, the sum of the measures of the angles of a triangle in degrees. So x = 180/20 = 9.

That means that the angle measurements are 3(9), 8(9) and 9(9) or 27, 72 and 81 degrees.