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.

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°