∠A and \angle B∠B are complementary angles. If m\angle A=(8x+27)^{\circ}∠A=(8x+27)
∘
and m\angle B=(6x-21)^{\circ}∠B=(6x−21)
∘
, then find the measure of \angle B∠B.
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Question
∠A and \angle B∠B are complementary angles. If m\angle A=(8x+27)^{\circ}∠A=(8x+27)
∘
and m\angle B=(6x-21)^{\circ}∠B=(6x−21)
∘
, then find the measure of \angle B∠B.
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Answer:
16
Step-by-step explanation:
(3x+9)+(6x+27)=
(3x+9)+(6x+27)=
\,\,180
180
supplementary angles add up to 180
3x+9+6x+27=
3x+9+6x+27=
\,\,180
180
Drop parentheses
9x+36=
9x+36=
\,\,180
180
Combine like terms
-36\phantom{=}
−36=
\,\,-36
−36
9x=
9x=
\,\,144
144
\frac{9x}{9}=
9
9x
=
\,\,\frac{144}{9}
9
144
Divide both sides by 9
x=
x=
\,\,\color{green}{16}
16
\text{Find the measure of }\angle A:
Find the measure of ∠A:
\text{m}\angle A=
m∠A=
\,\,3x+9
3x+9
Given
\text{m}\angle A=
m∠A=
\,\,3(\color{green}{16})+9
3(16)+9
Plug in x
\text{m}\angle A=
m∠A=
\,\,48+9
48+9
Multiply
\text{m}\angle A=
m∠A=
\,\,57
57
Combine
Answer:
∠ B = 15°
Step-by-step explanation:
Complementary angles sum to 90° , that is
∠ A + ∠ B = 90 , substitute values
8x + 27 + 6x – 21 = 90
14x + 6 = 90 ( subtract 6 from both sides )
14x = 84 ( divide both sides by 14 )
x = 6
Thus
∠ B = 6x – 21 = 6(6) – 21 = 36 – 21 = 15°