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The exterior angles of a triangle are in the ratio \(3:5:7\). What is the measure (in degrees) of the least interior angle of the triangle?

 

\(\phantom{3:4:5}\)

 
 Jun 23, 2022

Best Answer 

 #1
avatar+1746 
+2

Note that the exterior angles will always sum to \(360^ \circ\)

 

The ratio also has 15 "parts", meaning each part is \(360 \div 15 = 24\)

 

The smallest interior angle will always be supplementary to the largest exterior angle, which is \(7 \times 24 = 168\)

 

This means that the smallest interior angle is \(180 - 168 = \color{brown}\boxed{12}\)

 
 Jun 23, 2022
 #1
avatar+1746 
+2
Best Answer

Note that the exterior angles will always sum to \(360^ \circ\)

 

The ratio also has 15 "parts", meaning each part is \(360 \div 15 = 24\)

 

The smallest interior angle will always be supplementary to the largest exterior angle, which is \(7 \times 24 = 168\)

 

This means that the smallest interior angle is \(180 - 168 = \color{brown}\boxed{12}\)

 
BuilderBoi Jun 23, 2022

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