In triangle ABC, angle A is 6 times the measure of angle C, and angle C is twice the measure of angle B. What is the measure of angle B?

Question

In triangle ABC, angle A is 6 times the measure of angle C, and angle C is twice the measure of angle B. What is the measure of angle B?

Answer 1

In triangle ABC:

• angle A is 6 times the measure of angle C: A = 6C
• angle C is twice the measure of angle B: C = 2B

 

     A = 6C = 6*(2B) = 12B

     C = 2B

 

In a triangle, the internal angles add up to 180^o:

 

     A + B + C = 180^o

 

Now substitute 12B for A and 2B for C:

 

     12B + B + 2B = 180^o

     15B = 180^o

     B = 12^o

Answer 2

Lets use x for the angle we want to find:

  Angle B = x

Now that we have angle B (=x) we can use that to get angle C:

  Angle C = 2 times Angle B = 2x.

And then Angle A would be

  Angle A = 6 times Angle C = 6 * 2x = 12x

 

Now we have all three angles expressed in terms of x;

all together they have to add up to 180 degreees because it

is a triangle.  So we have:

 

  12x + 2x + x = 180

 

combining the x's:

 

  15x = 180

 

dividing by 15 on each side of the "=" gives:

 

  x = 180/15 = 12 degees = Angle B.