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 five times the measure of the first angle. The third angle is 26 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

F+S+T = 180

T=26+S

S+T = 5F

F = (S+T)/5 = (S+26+S)/5 = (2S + 26)/5

(2S+26)/5 + S + 26 + S =180

2S+26 + 10S = 154(5)

12S = 744

S=62 = y

T = S+26 = 88 = z

F= 2S+26)/5 = 150/5 = 30 = x

30, 62 and 88 degrees= x, y and z