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11 November, 05:34

A triangle is such that the largest angle is 7 times the smallest angle. The third angle is 15 less than the largest angle. Find the measure of each angle.

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  1. 11 November, 05:57
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    The smallest angle measures 13°, the largest angle measures 91° and the third angle measures 76°

    Step-by-step explanation:

    Let's recall that the interior angles of a triangle add up to 180°, therefore we have:

    Smallest angle = x

    Largest angle = 7x

    Third angle = 7x - 15

    Now, we can solve for x, using the following equation:

    x + 7x + 7x - 15 = 180

    15x = 180 + 15

    15x = 195

    x = 195/15

    x = 13 ⇒ 7x = 91 ⇒ 7x - 15 = 76

    The smallest angle measures 13°, the largest angle measures 91° and the third angle measures 76°
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