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30 December, 16:12

One angle of a triangle is three times as large as another. The measure of the third angle is 65 more than the smallest angle. What are the measures of each angle

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  1. 30 December, 16:22
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    Answer: the angles of the triangle are 23 degrees, 69 degrees and 88 degrees.

    Step-by-step explanation:

    Let x represent the measure of the smallest triangle.

    One angle of the triangle is three times as large as another. It means that the size of the larger angle is 3x.

    The measure of the third angle is 65 more than the smallest angle. This means that the measure of the third angle is

    x + 65

    The sum of the angles in a triangle is 180 degrees. It means that

    x + 3x + x + 65 = 180

    5x + 65 = 180

    5x = 180 - 65

    5x = 115

    x = 115/5

    x = 23 degrees

    The larger angle is

    3 * 23 = 69 degrees

    The third angle is

    23 + 65 = 88 degrees
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