If m angle 2 = 3x+1 and m angle 3 =2x+14 what is m angle 2

 m∡2 = 106° . 

Explanation:


Note that:   "∡2"   and  "∡3"  are "supplementary angles"; as shown in the diagram;  since both of them from a "straight line".

As such:   " m∡2  + m∡3 = 180 " .  

(Note:  The definition of supplementary angles.).

We are given:

 m∡2 = 3x + 1 ; 

 m∡3 = 2x + 4 ;

We are to find:  

  "m∡2" ;  or, "(3x + 1").

To begin:

Since:  "m∡2  + m∡3 = 180 " ;

We need to plug in our given values for:  
 
   "m∡2"   and   "m∡3" ; and set the equation equal to "180";
 and then "solve for "x" ;  

         m∡2  + m∡3  = 

        (3x + 1) + (2x +4) = 180 ;

         3x + 1  +  2x + 4  = 180 ;

  Combine the "like terms" on the left-hand side of the equation; to simplify:

       +3x +2x = 5x ;

       +1  + 4 = 5 ;

 And rewrite the equation as:

    5x + 5 = 180 ;

Subtract "5" from EACH side of the equation:

    5x + 5 − 5 = 180 − 5 ;

to get: 

   5x   =  175 ;

     Now, divide EACH SIDE of the equation by "5" ;
to isolate "x" on one side of the equation; and to solve for "x" ;

   5x / 5  = 175 / 5 ;

   to get:

   x = 35 . 

Now, the question asks, "What is m∡2 ?"

 We are given:

   " m∡2 = 3x + 1 " ;

         Since we know that "x = 35" (our solved value for "x"); 
we can plug in this value, "35" ;  
     for "x" ;  in the expression given that represents " m∡2 " ;
     to solve for " m∡2 " ;

   m∡2 = 3x + 1 = 3*(35)  + 1  = 105 + 1 = 106 .

 The answer is:  m∡2 = 106° .

Does this value make sense?  Let us check our work:

 If  "m∡2  +  m∡3 = 180 ; 

 then, " m∡3 = (180 − m∡2) = (180 −106) = 74 ; 

 Does  m∡3 = 174 ??

We are given:  "m∡3 = 2x + 4" ;  

Let us plug in our solved value, "35", for "x" in this expression;
   to see if  " m∡3 = 74 " ;

   m∡3 = 2x + 4  = 2*(35) + 4 = 70 + 4 = 74??  Yes!