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# Angles

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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

#1
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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
+2602
0

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