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20 September, 09:04

The exterior angle of a triangle is 119° and its interior opposite angle are in the ratio 8:9. Find the angle of a triangle

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  1. 20 September, 09:08
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    see explanation

    Step-by-step explanation:

    the ratio of the opposite interior angles = 8 : 9 = 8x : 9x

    The exterior angle of a triangle = sum of the opposite interior angles, hence

    8x + 9x = 119

    17x = 119 (divide both sides by 17)

    x = 7

    8 parts = 8x = 8 * 7 = 56

    9 parts = 9x = 9 * 7 = 63

    The sum of the 3 angles in a triangle = 180°

    subtract the sum of the 2 angles from 180 for third angle in triangle

    180° - (56 + 63) ° = 180° - 119° = 61°

    The 3 angles of the triangle are 56°, 61°, 63°
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