contestada

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.

Respuesta :

Answer:

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°