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 = 1/2zz = 2y
y = 3x1/3y = x

1/3y + y + 2y = 180multiply 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