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 30 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.

First angle = 30°

Second angle = 60°

Third angle = 90°

Step-by-step explanation:

x + y + z = 180

y + z = 5x

z = y + 30

then:

y + (y+30) = 5x

2y + 30 = 5x

x = (2y+30)/5

then:

x + y + z = 180

{(2y+30)/5} + y + y+30 = 180

{(2y+30)/5} + 2y + 30 = 180

{(2y+30)/5} = 180 - 30 - 2y

{(2y+30)/5} = 150 - 2y

2y+30 = 5(150-2y)

2y+30 = 5*150 + 5*-2y

2y+30 = 750 - 10y

2y + 10y = 750 - 30

12y = 720

y = 720/12

y = 60°

x = (2y+30)/5

x = (2*60 + 30)/5

x = (120+30)/5

x = 150/5

x = 30°

z = y + 30

z = 60 + 30

z = 90°

Check:

x + y + z = 180°

30° + 60° + 90° = 180°