SOLUTION: If the external angle of a triangle are in ratio 4:5:6, find the ratio of the triangle

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Question 1097155: If the external angle of a triangle are in ratio 4:5:6, find the ratio of the triangle
Found 2 solutions by Edwin McCravy, htmentor:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Let k be a number such that the angles are 
4k°, 
5k°, and 
6k° so they will be in the ratio 4:5:6

4k° + 5k° + 6k° = 180°
           15k° = 180°
             k° = 12°
              k = 12
  
The angles are 
4k° = 4(12)° = 48°, 
5k° = 5(12)° = 60°, and 
6k° = 6(12)° = 72°

Edwin
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
The sum of the exterior angles = 360
Let A = the smallest exterior angle
Then the other two angles are 5/4A and 6/4A
Find A:
A + 5/4A + 6/4A = 360
15/4A = 360
A = 96
The interior angles are, therefore, 180 - 96, 180 - (5/4)96, and 180 - (6/4)96
Interior angles: a = 84, b = 60, c = 36
So the ratio of the triangle is 60/84 = 5/7, 60/36 = 5/3, or 3:5:7
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