Two of the angles in a triangle 50° and 27°.find the measure of the third angle

The answer is: 53° .

Explanation: 

All three angles in ANY triangle add up to: 180° .

We are given the measurements of two of the angles in a triangle,
     50, and 27.  We know that the sum of the three (3) angles = 180.

We want the measurement  ofthe unknown angle, which we will represent with the variable, "x".

Method 1:

So, 50 + 27 + x = 180 ;

→ Subtract "50" and subtract "27" from EACH SIDE of the equation; 
         to isolate "x" on one side of our equation; and to solve for "x" ;

→ 50 + 27 + x − 50 − 27 = 180 − 50 − 27 ;  

    → to get:  x = 53° .

Method 2:

So, 50 + 27 + x = 180 ;

 → Add:  "50 + 27" ; to get, "77" ; 

→ Rewrite as: 77 + x = 180 ; 

→ Now, subtract "77" from EACH SIDE of the equation; 
         to isolate "x" on one side of our equation; and to solve for "x" ;

→   77 + x − 77 = 180 − 77 ;

→  to get:  x = 53° .

Method 3:

 → 180 − (50 + 27) = x ;  Solve for "x"

       → 50 + 27 = 77 ;
  
→ Rewrite the equation, substituting "77" in lieu of "(50 + 27)" ;
 
  → 180 − 77 = x ;  → 53 = x ;  ↔ x = 53° .

Method 4:

180 − (50 + 77) = x ; solve for 'x"; 

→ Note the "distributive property of multiplication:

      a*(b + c) = ab + ac ; AND:
  
      a*(b − c) = ab − ac ;

→ So, we have:  180 − (50 + 77) = x ;

Treat this as: " 180 − 1(50 + 77)" ;

→ Note, the coefficient "1" is implied; and makes since, since any value, multiplied by "1" equals that same value.

→ We treat this number as "-1", since there is a subtraction sign; so, let us consider the expression:  " -1(50 + 77) " 

    →   -1(50 + 77)  = (-1*50) + (-1*77) ;

    →  -50 + (-77) = -50 -77 = -127 ;

      →So rewrite the equation: Bring down the "180";
                                      & bring down the "-127" and the: "= x " ; 

           → 180 − 127 = x ;  to get: →  53 = x ;   ↔   x = 53° . 

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