Question

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?

Answer 1

23°

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°