Solve to find the measure B: m(A) is 3 times m(B), and....

[Alex22]

Hey, Im having a bit of trouble trying to solve this question. If anyone could help I would greatly appreciate it! thanks.

The measure of angle A is three times the measure of angle B , and the measure of angle B is three times the measure of angle C. If angle A and angle C are complementary, find the measure of angle B.

 

[Loren]

Re: Solve to find the measure.

The measure of angle A is three times the measure of angle B , and the measure of angle B is three times the measure of angle C. If angle A and angle C are complementary, find the measure of angle B.

Let's see. Complementary means that their sum is 90°. That will help you to write one equation involving A and C.
Measure of angle B equals 3 times the measure of angle C. That is information to write an equation involving B and C.
A is three times the measure of angle B. That is the basis for you to write an equation involving B and C.

That gives you 3 equations in 3 unknowns which will allow you to solve for all three angles.

If you cannot solve a simultaneous system of equations then you must name things in terms of only one variable. You could start by saying...

Let x represent the measure of angle C.
Then on the basis of the words "the measure of angle B is three times the measure of angle C" you can say that...
B = 3x
On the basis of the words "measure of angle A is three times the measure of angle B" you can write...
A = 3B = 3(3x) = 9x.

And you can take it from there?

 

[Denis]

A nutter way:
A = 3B, so B = A/3
B = 3C, so A/3 = 3C, so A = 9C
A + C = 90, so 9C + C = 90 .... carry on

 

[masters]

\(\displaystyle A=3B\)

\(\displaystyle B=3C\), which makes \(\displaystyle C=\frac{B}{3}\)

\(\displaystyle A+C=90\)

Substituting,

\(\displaystyle 3B+\frac{B}{3}=90\)

Multiply both sides by 3,

\(\displaystyle 9B+B=270\)

\(\displaystyle 10B=270\)

\(\displaystyle \boxed{B=27}\)

\(\displaystyle A=3B\Longrightarrow A=3(27)\Longrightarrow \boxed{A=81}\)

\(\displaystyle C=\frac{B}{3}\Longrightarrow C=\frac{27}{3}\Longrightarrow \boxed{C=9}\)