SOLUTION: In a triangle. The one angle of triangle is two times smallest an another three times smallest. Find all the angles of the triangle???

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Question 1044710: In a triangle. The one angle of triangle is two times smallest an another three times smallest. Find all the angles of the triangle???
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the smallest angle be alpha
if the angle beta of triangle is two+times smallest,than we have beta=2%2Aalpha and if gamma three times smallest we have gamma=3%2Aalpha
since the sum of all angles in triangle is 180°, we have
alpha%2Bbeta%2Bgamma=180°........substitute beta and gamma
alpha%2B2%2Aalpha%2B3%2Aalpha=180°
6%2Aalpha=180°
alpha=180%2F6°
alpha=30°->the smallest angle
now find other two angles:
beta=2%2Aalpha-> beta=2%2A30°-> beta=60°

gamma=3%2Aalpha->gamma=3%2A30°->gamma=90°