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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?

May 3, 2022

#1
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We know that the exterior angles of the triangle add to 360.

$$3 + 5 + 7 = 15$$. This means that 1 is $$360 \div 15 = 24$$

The smallest interior angle is supplementary to the largest exterior angle.

The largest exterior angle is $$24 \times 7 = 168$$

Can you find the interior angle now?

May 3, 2022