The figure is a parallelogram.

Mathematics

2 answers:

slavikrds [6]3 years ago

6 0

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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Let us check our answer:
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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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