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?

Guest 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 180^{o}, each part equals 180/12 which is 15.

So 3 x 15 = 45^{o}

and 4 x 15 = 60^{o}

and 5 x 15 = 75^{o}

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

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Guest Apr 9, 2020