Q:

# 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°

Accepted Solution

A:
Answer:  " m∠ACD = 40° " .
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Explanation:
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We are asked to find:  "m∠ACD" ;
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Note:  m∠ACD  =  m∠ABD ;
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So, given:

m∠ACD  =  (4x + 4)° ;

m∠ABD =   (6x - 14)° ;
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4x + 4 = 6x - 14 ;

Solve for "x" ; then solve for:  "m∠ACD"  ;
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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" ;
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2x / 2 = 18/2 ;

x = 9 .
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Now, to solve for:  " m∠ACD "  :
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m∠ACD =  (4x + 4)°  ;

Substitute "9" for "x" ;

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