The measures of the three angles of a triangle are given by 3x + 1, 2x - 3, and 9x. What is the measure of the smallest angle?

23°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

3x + 1 + 2x - 3 + 9x = 180 (simplify left side)

14x - 2 = 180 (add 2 to both sides)

14x = 182 (divide both sides by 14)

x = 13

The 3 angles are

3x + 1 = (3 * 13) + 1 = 39 + 1 = 40°

2x - 3 = (2 * 13) - 3 = 26 - 3 = 23° ← smallest angle

9x = 9 * 13 = 117°