Question

LN bisects KLM into two congruent angles measuring (3x-4) and (4x-27). Find klm

Answer 1

Answer:  The m ∡KLM is:  130° .
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Explanation:
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(3x − 4) = (4x − 27) ;  (Since these are "bisected, congruent angles", they are equal).

⇒ 3x − 4 = 4x − 27 ;

⇒ Subtract "4x" from  EACH SIDE of the equation; and add "4" to EACH SIDE of the equation;

⇒    3x − 4 − 4x + 4 = 4x − 27 − 4x + 4 ;

to get:

⇒  - 1x = -23 ;

⇒  Divide EACH SIDE of the equation by "-1" ; to isolate "x" on one side of the equation; and to solve for "x" ;

⇒  -1x / -1 = -23 / -1 ;  to get:

⇒  x = 23;
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To find m ∡KLM :

m ∡ KLM = (3x − 4) + (4x − 27) ;

{Note:  Remember:  (3x − 4) = (4x − 27) } ;

So, plug in our solved value for "x" ; which is: "x = 23" into one of the expressions for one of the congruent angles.

Let us start with: "(3x − 4)" . 

(3x − 4) = 3x − 4 = 3(23) − 4 = 69 − 4 = 65 .

By plugging in our solve value for "x" ; which is: "x = 23" ; into the expression for the other congruent angle, we should get: "65" ;

Let us try:

(4x − 27) = 4x − 27 = 4(23) − 27 = 92 − 27 = 65.  Yes!
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So to find m ∡KLM:

(3x − 4) + (4x − 27) = 65 + 65 = 130° .
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Alternate method:
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At the point which we have:
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To find m ∡KLM :

m ∡ KLM = (3x − 4) + (4x − 27) ; and at which we have our solved value for "x" ; which is:  "x = 23" ;
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We can simply plug in our known value for "x" ; which is:  "23" ; into the following:
m ∡ KLM = (3x − 4) + (4x − 27) = [(3*23) − 4] + [(4*23) − 27] ;
                                                   = (69 − 4) + (92 − 7) = 65 + 65 = 130° .
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{Note:  Using this method, we determine that each angle is equal; that is, "65° ".}.
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