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10 December, 09:56

The exterior angles of a triangle are in the ratio of 4:5:6. What is the least interior angle

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  1. 10 December, 11:11
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    Least interior angle = 36 degrees

    Step-by-step explanation:

    The ratio 4:5:6 means that the greatest exterior angle is 6 / (4+5+6) = 6/15 of the total value of the angles.

    The sum of the exterior angles = 360 degrees so the greatest one is

    = 360 * 6 / 15

    = 360 * 2/5

    = 144 degrees

    This is adjacent to the smallest interior angle of the triangle so the answer is 180 - 144 = 36 degrees
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