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The exterior angles of a triangle are in the ratio 3:4:5  What is the measure (in degrees) of the least interior angle of the triangle?

 Apr 9, 2020
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The exterior angles of a triangle are in the ratio 3:4:5  What is the measure (in degrees) of the least interior angle of the triangle? 

 

Well, a triangle doesn't have exterior angles, but if it did they'd be vertical angles of the interior angles and therefore the same.  So let's figure the interior angles of a triangle in the ratio 3:4:5. 

 

3 + 4 + 5 = 12 so there are 12 parts to divvy up.  Since the interior angles of a triangle total 180o, each part equals 180/12 which is 15. 

 

So             3 x 15 = 45o 

and           4 x 15 = 60o 

and           5 x 15 = 75o 

 

And there you go, your three angles in the ratio 3:4:5 and the smallest one is 45o  

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 Apr 9, 2020

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