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7 November, 13:48

A

∠A and



B

∠B are complementary angles. If m



A

=

(

5

x

-

27

)



∠A = (5x-27)



and m



B

=

(

4

x

-

27

)



∠B = (4x-27)



, then find the measure of



A

∠A.

+3
Answers (1)
  1. 7 November, 15:12
    0
    see explanation

    Step-by-step explanation:

    Complementary angles sum to 90°, thus

    ∠A ∠B = 90 ← substitute values

    5x - 27 + 4x - 27 = 90, that is

    9x - 54 = 90 (add 54 to both sides)

    9x = 144 (divide both sides by 9)

    x = 16

    Hence

    ∠A = 5x - 27 = (5 * 16) - 27 = 80 - 27 = 53°

    ∠B = 4x - 27 = (4 * 16) - 27 = 64 - 27 = 37°
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