Question

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Answer 1

The answer: m∡BCD = 130° .
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Explanation:
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m∡BCD = 9x - 5 = our answer.
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Note: (9x - 5) + (m∡C IN Δ  ACB)= 180 ;
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Reason: all angles on straight line add up to 180.
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Note: In Δ ACB; m∡A + m∡B + m∡c = 180.
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Reason: All three angles in any triangle add up to 180.
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Given  Δ ACB, we are given:
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m∡C= ?
m∡B = (4x + 5)
m∡A = 65
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So, given  Δ ACB; m∡A + m∡B + m∡c = 180;
 →Plug in our known values and rewrite:
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Given  Δ ACB; 65 + 4x + 5 + (m∡c) = 180;
  →Simplify, and rewrite:
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Given  Δ ACB; 4x + 70 + (m∡c) = 180;
  →Subtract "70" from each side of the equation; and rewrite:
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Given  Δ ACB; 4x + (m∡C) = 110;
   →Subtract "4x" from EACH SIDE of the equation; to isolate: "(m∡c)" on one side of the equation; and "solve in terms of "(m∡C)" ;
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Given Δ ACB' m∡C = 110 - 4x ;
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So, we know that: (110 - 4x) + (9x - 5) = 180; (since all angles on a straight line add up to 180.
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We can solve for "x".
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(110 - 4x) + (9x - 5) = 180;
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Rewrite as: 
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(110 - 4x) + 1(9x - 5) = 180 ;  (Note: there is an implied coefficient of "1"; since anything multiplied by "1" equals that same value).
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Note the "distributive property of multiplication": 
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 a*(b+c) = ab + ac ; AND:
 a*(b - c) = ab - ac .
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So, +1(9x - 5) = (+1*9x) - (+1*5) = 9x - 5 ;
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So we can rewrite:
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(110 - 4x) + (9x - 5) = 180 ; as:
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110 - 4x + 9x - 5 = 180 ;  We can simplify this by combining "like terms" on                                         the "left-hand side" of the equation:
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110 - 5 = 105 ;
-4x + 9x = 5x; 
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So, rewrite as: 5x + 105 = 180;  Subtract "105" from EACH side; to get:
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 5x  = 75 ; Now, divide each side of the equation by "5"; 
              to get: x = 15.
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Now, we want to know: m∡BCD; which equals:
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 9x - 5 ;  let us substitute "15" for "x"; and solve:
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9x - 5 = 9*(15) - 5 = 135 - 5 = 130.
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The answer: m∡BCD = 130°
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