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8 August, 04:27

The larger of two supplementary angles measures 20° less than four times the measures of the smaller angle. find the degree measure of each angle

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  1. 8 August, 04:44
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    Supplementary angles by definition means the sum is 180.

    From that knowledge we can write up some equations.

    Let angle 1 = x, and angle 2 = y

    x + y = 180

    "The larger of two supplementary angles measures 20° less than four times the measure of the smaller angle"

    (Let x be the larger angle)

    x+20 = 4y

    Since there are two different equations, and two variables, this means we have a set of simultaneous equations.

    We can solve this via the substitution method or the elimination method.

    I choose to solve it via the substitution method cause of personal preference.

    x + y = 180 = > x = 180 - y

    x+20 = 4y = > x = 4y - 20

    Make them equal each other ...

    180 - y = 4y - 20

    200 = 5y

    40 = y

    Now that we know y we can sub it into any equation to find x

    x + 20 = 4y

    x + 20 = 4 (40)

    x + 20 = 160

    x = 140

    So the angles are 40° and 140°
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