SOLUTION: One angle if a triangle is twice another. The third angle is three times the smallest. Find the measure of the smallest angle.

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Question 65881: One angle if a triangle is twice another. The third angle is three times the smallest. Find the measure of the smallest angle.
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
One angle of a triangle is twice another.
The third angle is three times the smallest. 
Find the measure of the smallest angle.

Let the smallest angle be A
Let the middle-sized angle be B
Let the largest angle be C.

There are two possibilities because the first 
sentence is ambiguous.

1. If the middle-sized angle is twice the 
   smallest angle, then,

B = 2A
C = 3A
A + B + C = 180

Do you know how to solve that system of
equations?  If not post again asking how.

Solve that system and get

A = 30°, B = 60°, C = 90°

so the smallest angle is A or 30°.

------------------------------------------

2. If the largest angle is twice the 
   middle-sized angle, then

C = 2B
C = 3A
A + B + C = 180

Solve that system and get:

A = 32 8/11°, B = 49 1/11°, 98 2/11°

so the smallest angle is 32 8/11°

Edwin
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