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?
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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