in a triangle given that angle a -angle b =33 and angle b-angle c = 15 .find the measures of all angles

Question

Answer urgent 

Answer 1

Emily, i think you may have misread part of the question. I belive tbat b - c = 15, 

 

 But the process is right: all triangles have 3 angles whose sum is 180 degrees, and by substituting one variable for another, you can work the angles out one at a time.

 

If a - b = 33, then you can say that a = 33 + b.

 

You can also see that b = 15 + c.

 

Soon you'll see how all 3 variables can be expressed in terms of c. Then you'll solve for c, then work backwards to find the others.

 

Good luck!

 

Answer 2

a-b=33.  c=15.  a+b+c=180

 

a+b+15=180

      - 15  -15

a+b      =165

 

Subtract the two similar formulas:

   a-b=   33

-  a+b=165

  -2b   =-132

   -2       -2

    b    =66

 

Plug back in

a +b  +c  =180

a+ 66+15=180

a+81       =180

   -81          -81

      a      =99

 

Double check:

a-b=33

99-66=33

Answer 3

a+b+c=180

a-b=33

b-c=15

a=33+b from a-b=33

c=b-15 from b-c=15

substitute into a+b+c=180

(33+b)+b+(b-15)=180

33+b+b+b-15=180

18+3b=180

3b=180-18

3b=162

b=162/3

b=54º

a-54=33

a=54+33

a=87º

87+54+c=180

141+c=180

c=180-141

c=39º