Find the measures of the three angles.

Question

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second.

Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

Answer 1

x + y + z = 180

The sum of the measures of the second and third angles is three times the measure of the first angle

y + z = 3x, x = (y + z)/3

The third angle is 15 more than the second

z = y + 15

Substitute:

(y + z)/3 + y + y + 15 = 180

y + z + 3y + 3y + 45 = 540

7y + z = 495

Substitute again:

7y + y + 15 = 495

8y = 480

y = 60

z = 75

x = 45