A+b=180A=-2x+115B=-6x+169What is the value of B?

The answer is:  " 91 " .   
___________________________________________________
                    →    " B = 91 " .
__________________________________________________ 

Explanation:
__________________________________________________
Given:  
__________________________________________________
    "  A +  B = 180 " ;

  "A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;  
_____________________________________________________
METHOD 1)
_____________________________________________________
Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to  solve for "B"
_____________________________________________________

(115 − 2x) + (169 − 6x) = 

  115 − 2x + 169 − 6x = ?

→ Combine the "like terms" ;  as follows:

      + 115 + 169 = + 284 ; 

 − 2x − 6x = − 8x ; 
_________________________________________________________
And rewrite as:

 " − 8x + 284 " ; 
_________________________________________________________
   →  " - 8x + 284 = 180 " ; 

Subtract:  "284" from each side of the equation:

  →  "  - 8x + 284 − 284 = 180 − 284 " ; 

to get:

 →  " -8x = -104 ; 

Divide EACH SIDE of the equation by "-8 " ; 
    to isolate "x" on one side of the equation; & to solve for "x" ; 

→ -8x / -8 = -104/-8 ; 

→  x = 13
__________________________________________________________
Now, to find the value of "B" :
__________________________________________________________
  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;  

↔  B = 169 − 6x ;  

         = 169 − 6(13) ;   ===========> Plug in our "solved value, "13",  for "x" ;

         = 169 − (78) ; 

         = 91 ;

   B   = " 91 " .
__________________________________________________
The answer is:  " 91 " . 
____________________________________________________
     →     " B = 91 " . 
____________________________________________________
Now;  let us check our answer:
____________________________________________________
               →   A + B = 180 ;  
____________________________________________________
Plug in our "solved answer" ; which is "91", for "B" ;  as follows:
________________________________________________________

→  A + 91 = ? 180? ;  

↔  A = ? 180 − 91 ? ; 

→  A = ?  -89 ?  Yes!
________________________________________________________
→  " A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

Plug in our solved value for "x"; which is: "13" ; 

" A = 115 − 2x " ; 

→  A = ? 115 − 2(13) ? ;

→  A = ? 115 − (26) ? ; 

→  A = ? 29 ? Yes!
_________________________________________________ 
METHOD 2)
_________________________________________________
Given:  
__________________________________________________
    "  A +  B = 180 " ;

  "A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; 

→  Solve for the value of "B" :
_______________________________________________________
 A + B = 180 ;  

→ B = 180 − A ; 

→ B = 180 − (115 − 2x) ; 

→ B = 180 − 1(115 − 2x) ;  ==========> {Note the "implied value of "1" } ; 
__________________________________________________________
Note the "distributive property" of multiplication:__________________________________________________  a(b + c)  = ab +  ac ;  AND:
  a(b − c)  = ab − ac .________________________________________________________
Let us examine the following part of the problem:
________________________________________________________
              →      " − 1(115 − 2x)  " ; 
________________________________________________________

→  "  − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;

                                =  -115 − (-2x) ;
                         
                                =  -115  +  2x ;        
________________________________________________________
So we can bring down the:  " {"B = 180 " ...}"  portion ; 

→and rewrite:
_____________________________________________________

→  B = 180 − 115 + 2x ; 

→  B = 65 + 2x ; 
_____________________________________________________
Now;  given:   "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; 

→ " B =  169 − 6x  =  65 + 2x " ; 
______________________________________________________
→  " 169 − 6x  =  65 + 2x "

Subtract "65" from each side of the equation;  & Subtract "2x" from each side of the equation:

→  169 − 6x − 65 − 2x  =  65 + 2x − 65 − 2x ; 

to get:

→   " - 8x + 104 = 0 " ;
 
Subtract "104" from each side of the equation:

→   " - 8x + 104 − 104 = 0 − 104 " ;

to get: 

→   " - 8x = - 104 ;

Divide each side of the equation by "-8" ; 
   to isolate "x" on one side of the equation; & to solve for "x" ; 

→  -8x / -8  = -104 / -8 ; 

to get:

→  x =  13 ; 
______________________________________________________

Now, let us solve for:  " B " ;  → {for which this very question/problem asks!} ; 

→  B = 65 + 2x ;  

Plug in our solved value, " 13 ",  for "x" ; 

→ B = 65 + 2(13) ; 

        = 65 + (26) ;  

→ B =  " 91 " .
_______________________________________________________
Also, check our answer:
_______________________________________________________
Given:  "B = - 6x + 169 " ;   ↔  B = 169 − 6x = 91 ; 

When "x  = 13 " ; does: " B = 91 " ? 

→ Plug in our "solved value" of " 13 " for "x" ;

      → to see if:  "B = 91" ; (when "x = 13") ;

→  B = 169 − 6x ; 

         = 169 − 6(13) ; 

         = 169 − (78)______________________________________________________
→ B = " 91 " . 
______________________________________________________