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16 March, 19:18

The ratio of two complementary angles is 15:30. what is the measure of the smaller angle?

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  1. 16 March, 19:21
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    75 degrees

    Step-by-step explanation:

    if the angles are complementary, then their sum is 90 degrees.

    let x = one of the angles and let y = the other.

    you get:

    x + y = 90

    one of the angles is in the ratio of 1:5 with the other angle.

    let x be that angle.

    ratio formula says x/y = 1/5

    solve for x to get x = (1/5) * y

    replace y in the formula of x + y = 90 to get:

    (1/5) * y + y = 90

    combine like terms to get (6/5) * y = 90

    multiply both sides of equation by (5/6) to get:

    y = (5/6) * 90 = 75 degrees.

    since x + y = 90, then x must be 15 degrees.

    x = 15

    y = 75

    x/y = 15/75 = 1/5

    looks good.

    the angles measure 15 degrees and 75 degrees.
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