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.

1. Calantha

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

2. thanhha

∠ 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°