Mathematics

Question

Complemetary angles are two angles whose measures add up to 90 degrees. The ratio of the measures of two complementary angles is 2:13. What are the measures of the angles?

2 Answer

  • Let A and B be the two complementary angles.

    A = smaller angle = 2x

    B = larger angle = 13x

    x = some unknown number

    Note how the ratio A:B turns into 2x:13x which simplifies to 2:13

    A+B = 90 ... because the angles are complementary

    2x+13x = 90 ... substitution

    15x = 90

    x = 90/15

    x = 6

    A = 2*x = 2*6 = 12 degrees

    B = 13*x = 13*6 = 78 degrees

    The two angles are 12 degrees and 78 degrees.

    Check:

    A/B = 12/78 = (2*6)/(13*6) = 2/13, so A:B = 2:13

    A+B = 12+78 = 90

  • Answer:

    K

    Step-by-step explanation:

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