One angle in a triangle is half the largest angle, but three times the smallest. find all three angles.

X = smallest angle, y = middle angle, z = largest angle

x + y + z = 180 ... interior angles of a triangle add up to 180 degrees

y = 1/2z ... z = 2y

y = 3x ... 1/3y = x

1/3y + y + 2y = 180 ... multiply everything by 3

y + 3y + 6y = 540

10y = 540

y = 540/10

y = 54 < = = the middle angle

z = 2y

z = 2 (54)

z = 108 < = = = largest angle

1/3y = x

1/3 (54) = x

54/3 = x

18 = x < = = = smallest angle