Answer:
12 ft 2 in.
Step-by-step explanation:
Conversion: 1 ft = 12 in.
Add the lengths of the boards.
4 ft 10 in. + 2 ft 11 in. + 4 ft 5 in. =
= 4 ft + 2 ft + 4 ft + 10 in. + 11 in. + 5 in.
= 10 ft + 26 in.
= 10 ft + 24 in. + 2 in.
Since 1 ft = 12 in., then 24 in. = 2 ft.
= 10 ft + 2 ft + 2 in.
= 12 ft 2 in.
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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 = <span>(6x - 14)° ;
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4x + 4 = 6x - 14 ;
Solve for "x" ; then solve for: "m</span>∠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<span>∠ACD " :
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m∠ACD = <span>(4x + 4)° ;
Substitute "9" for "x" ;
</span>
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<span>∠ABD = (6x - 14) ;
</span>m∠ACD = ∠ABD ;
<span>
Since </span>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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