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°