Algebra 1 Question

Question

How do you answer this question?

 

In any triangle, the sum of the measures of the angles is 180 degrees. In triangle ABC, angle A is twice as large as angle B. Angle B is 4 degrees larger than angle C. Find the measure of each angle.

Answer 1

Hello there, Emma

 

There are different ways to set the problem up. The smallest angle is c, then b, and a is the largest angle according to the information you provided.So,

 

Let x           be the measure of angle c

Let x+4      be the measure of angle b, since b is 4 degrees larger than c.

Let 2(x+4) be the measure of angle c, since it is twice as big as b.

 

So, angle a+ angle b+ angle c= 180    Substituting

      2(x+4) + (x+4)+ x          =180

      2x+8+x+4+x = 180                    Using the distributive property.

               4x+12= 180                       Combining like terms

                   -12     -12                      Subtracting 8 from both sides

                   4x= 168                        Dividing both sides by 4

                      x= 42

c= 42

b= x+4= 42+4= 46

a=2(x+4)= 2(42+4)= 2(46)= 92

 

So, the measurements for a, b, c are 92,46, 42, respectively.

 

I hope this helps.  Please rate my answer :)

 

D. Y. Taylor

 

Answer 2

Because of the nature of a triangle we know that A + B + C = 180.

 

The problem also allows us to make the following equations:

 

1. A = 2B

2. B = C + 4

    C = B - 4

 

We can input these two new equations into the original one in order to solve for B:

 

2B + B + (B - 4) = 180

4B - 4 = 180

4B = 184

B = 46

 

From that we know:

 

C = B - 4

C = 42

 

We also know:

 

A = 2B

A = 92

Answer 3

A = 2B

B = 4 + C        -----------> C = B - 4

 

A + B + C = 180

 

 2B + B + (B - 4) = 180

 

4B - 4 = 180

 

4B = 184

 

B  = 46 figure out the other angles.