What is m∠knl?

explain how as well

 m∠KNL = 102° .

Explanation: 

 m∠KNL = m∠JNM ;  Reason: These angles are vertical; and vertical angles                                      are congruent.

Given: 

m∠KNL = 3 (x + 14) ;  and:

m∠JMN = 5x + 2 ;

And we want to solve for:

m∠KNL = 3 (x + 14) ; 

And both of these angles are congruent; 

We set this expressions equal to each other; Then solve for "x"; then plug that solved value into "x" into the expression for "m∠KNL" ; to solve for "m∠KNL" ; 

As such: 

3 (x + 14) = 5x + 2 ;

We expand:

3 (x + 14) ;  Using the "distributive property of multiplication": 

    a(b + c) = ab + ac ; 

So, m∠KNL = 3 (x + 14) = (3*x) + (3*14) = 3x + 42 ; 

And rewrite the equation as:

3x + 42 = 5x + 2 ; 

Subtract "3x" and "2" from each side of the equation;

  3x + 42 − 3x − 2 = 5x + 2 − 3x − 2 ;

to get:

 40 = 2x ;

↔  2x = 40 ;

 Now, divide EACH side of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ; 

    2x / 2 = 40 / 2 ;

         x = 20 . 

Now, to solve for m∠KNL ;

From above:

m∠KNL = 3 (x + 14) = (3*x) + (3*14) = 3x + 42 ;


→ m∠KNL = 3 (x + 14) = 3x + 42 ; 

Substitute: "20" for "x" 

3*(20 + 14) = 3*34 = 102 ;

Check using "3x + 42" ;
  
(3*20) + 42 = 60 + 42 = 102.

Also, m∠JMN = 5x + 2 =? 102?  It should.

Let us check, substituting "20" for "x".

5x + 2 =? 102?

(5*20) + 2 =? 102?

(100) + 2 =? 102? Yes!

So;  m∠KNL = 102° .

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