Question

A triangle is such that the largest angle is 3 times the smallest angle. The third angle is 23 less than the largest angle. Find the measure of each angle.

Answer 1

largest angle: 3x

smallest angle: x

third angle: 3x - 23

The sum of the angles of a triangle equals 180°

(3x) + (x) + (3x -23) = 180

7x - 23 = 180

7x = 203

x = 29

largest angle: 3x = 3(29) = 87

third angle: 3x - 23 = 3(29) - 23 = 87 - 23 = 64

Answer: 29°, 64°, 87°