The answer is:  " 91 " . Â
          →   " B = 91 " .
Â
Explanation:
Given: Â
  "  A +  B = 180 " ;
 "A =  -2x + 115 " ;   ↔  A =  115 − 2x ; Â
 "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; Â
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) =Â
 115 − 2x + 169 − 6x = ?
→ Combine the "like terms" ;  as follows:
   + 115 + 169 = + 284 ;Â
 − 2x − 6x = − 8x ;Â
And rewrite as:
 " − 8x + 284 " ;Â
  →  " - 8x + 284 = 180 " ;Â
Subtract: Â "284" from each side of the equation:
  →  "  - 8x + 284 − 284 = 180 − 284 " ;Â
to get:
 →  " -8x = -104 ;Â
Divide EACH SIDE of the equation by "-8 " ;Â
  to isolate "x" on one side of the equation; & to solve for "x" ;Â
→ -8x / -8 = -104/-8 ;Â
→  x = 13
Now, to find the value of "B" :
  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; Â
↔  B = 169 − 6x ; Â
     = 169 − 6(13) ;  > Plug in our "solved value, "13",  for "x" ;
     = 169 − (78) ;Â
     = 91 ;
   B  = " 91 " .
The answer is:Â Â "Â 91Â " .Â
   →    " B = 91 " .Â
Now; Â let us check ourÂ
        →  A + B = 180 ; Â
Plug in our "solved answer" ; which is "91", for "B" ; Â as follows:
→  A + 91 = ? 180? ; Â
↔  A = ? 180 − 91 ? ;Â
→  A = ?  -89 ?  Yes!
→  " A =  -2x + 115 " ;   ↔  A =  115 − 2x ; Â
Plug in our solved value for "x"; which is: "13" ;Â
" A = 115 − 2x " ;Â
→  A = ? 115 − 2(13) ? ;
→  A = ? 115 − (26) ? ;Â
→  A = ? 29 ? Yes!
Â
METHOD 2)
Given: Â
  "  A +  B = 180 " ;
 "A =  -2x + 115 " ;   ↔  A =  115 − 2x ; Â
 "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;Â
→  Solve for the value of "B" :
 A + B = 180 ; Â
→ B = 180 − A ;Â
→ B = 180 − (115 − 2x) ;Â
→ B = 180 − 1(115 − 2x) ;  > {Note the "implied value of "1" } ;Â
Note the "distributive property" of multiplication:Â a(b + c) Â = ab + Â ac ; Â AND:
 a(b − c)  = ab − ac .
Let us examine the following part of the problem:
       →    " − 1(115 − 2x)  " ;Â
→  "  − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;
                =  -115 − (-2x) ;
            Â
                =  -115  +  2x ;    Â
So we can bring down the: Â " {"B = 180 " ...}" Â portion ;Â
→and rewrite:
→  B = 180 − 115 + 2x ;Â
→  B = 65 + 2x ;Â
Now;  given:  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;Â
→ " B =  169 − 6x  =  65 + 2x " ;Â
→  " 169 − 6x  =  65 + 2x "
Subtract "65" from each side of the equation; Â & Subtract "2x" from each side of the equation:
→  169 − 6x − 65 − 2x  =  65 + 2x − 65 − 2x ;Â
to get:
→  " - 8x + 104 = 0 " ;
Â
Subtract "104" from each side of the equation:
→  " - 8x + 104 − 104 = 0 − 104 " ;
to get:Â
→  " - 8x = - 104 ;
Divide each side of the equation by "-8" ;Â
  to isolate "x" on one side of the equation; & to solve for "x" ;Â
→  -8x / -8  = -104 / -8 ;Â
to get:
→  x =  13 ;Â
Now, let us solve for:  " B " ;  → {for which this very question/problem asks!} ;Â
→  B = 65 + 2x ; Â
Plug in our solved value, " 13 ", Â for "x" ;Â
→ B = 65 + 2(13) ;Â
    = 65 + (26) ; Â
→ B =  " 91 " .
Also, check our
Given:  "B = - 6x + 169 " ;   ↔ B = 169 − 6x = 91 ;Â
When "x  = 13 " ; does: " B = 91 " ?Â
→ Plug in our "solved value" of " 13 " for "x" ;
   → to see if:  "B = 91" ; (when "x = 13") ;
→  B = 169 − 6x ;Â
     = 169 − 6(13) ;Â
     = 169 − (78)
→ B = " 91 " .Â