the figure is a parallelogram.
the m∠acd = (4x + 4)° and m∠abd = (6x - 14)°. find m∠acd.
a) 9°
b) 24°
c) 40°
d) 60°

  " m∠ACD = 40° " .

Explanation:

We are asked to find:  "m∠ACD" ; 

Note:  m∠ACD  =  m∠ABD ; 

So, given: 

m∠ACD  =  (4x + 4)° ;

m∠ABD =   (6x - 14)° ;

  4x + 4 = 6x - 14 ;

Solve for "x" ; then solve for:  "m∠ACD"  ;

 Add "14" to each side of the equation; and subtract "4x" from each side of the equation ; 

  4x + 4 + 14 - 4x  = 6x - 14 + 14 - 4x  ;

to get:

18 = 2x ;

↔  2x = 18 ;

Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" ;

     2x / 2 = 18/2 ;

      x = 9 .

Now, to solve for:  " m∠ACD "  :

      m∠ACD =  (4x + 4)°  ;

Substitute "9" for "x" ; 

      m∠ACD = (4*9) + 4 = 36 + 4 = 40° .

 " m∠ACD = 40° " .

Let us check our

m∠ACD = 40 ; and m∠ABD = (6x - 14) ;

m∠ACD = ∠ABD ; 

Since m∠ABD = (6x - 14) ;  

If x = 9;  if we plug in "9" into the expression for "m∠ABD" ; will the value obtained be "40" ??

m∠ABD = (6x - 14) ;  Let us plug in "9" for "x" ; to see if the value obtained is "40"

6x - 14 = ? (6*9) - 14 ??
 
6x - 14 = ?  54 - 14 ??

6x - 14 = ? 40 ?? Yes!

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