A

∠A and

∠

B

∠B are complementary angles. If m

∠

A

=

(

4

x

-

1

)

∘

∠A = (4x-1)

∘

and m

∠

B

=

(

5

x

+

19

)

∘

∠B = (5x+19)

∘

, then find the measure of

∠

B

∠B.

see explanation

Step-by-step explanation:

Complementary angles sum to 90°, hence

∠A + ∠B = 90° ← substitute values

4x - 1 + 5x + 19 = 90, that is

9x + 18 = 90 (subtract 18 from both sides)

9x = 72 (divide both sides by 9)

x = 8

Hence

∠A = 4x - 1 = (4 * 8) - 1 = 32 - 1 = 31°

∠B = 5x + 19 = (5 * 8) + 19 = 40 + 19 = 59°