Answer: m∡2 = 106° .
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Explanation:
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Note that: "∡2" and "∡3" are "supplementary angles"; as shown in the diagram; since both of them from a "straight line".
As such: " m∡2 + m∡3 = 180 " .
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(Note: The definition of supplementary angles.).
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We are given:
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m∡2 = 3x + 1 ;
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m∡3 = 2x + 4 ;
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We are to find:
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"m∡2" ; or, "(3x + 1").
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To begin:
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Since: "m∡2 + m∡3 = 180 " ;
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We need to plug in our given values for:
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"m∡2" and "m∡3" ; and set the equation equal to "180";
and then "solve for "x" ;
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m∡2 + m∡3 =
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(3x + 1) + (2x +4) = 180 ;
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3x + 1 + 2x + 4 = 180 ;
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Combine the "like terms" on the left-hand side of the equation; to simplify:
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+3x +2x = 5x ;
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+1 + 4 = 5 ;
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And rewrite the equation as:
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5x + 5 = 180 ;
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Subtract "5" from EACH side of the equation:
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5x + 5 − 5 = 180 − 5 ;
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to get:
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5x = 175 ;
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Now, divide EACH SIDE of the equation by "5" ;
to isolate "x" on one side of the equation; and to solve for "x" ;
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5x / 5 = 175 / 5 ;
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to get:
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x = 35 .
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Now, the question asks, "What is m∡2 ?"
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We are given:
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" m∡2 = 3x + 1 " ;
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Since we know that "x = 35" (our solved value for "x");
we can plug in this value, "35" ;
for "x" ; in the expression given that represents " m∡2 " ;
to solve for " m∡2 " ;
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m∡2 = 3x + 1 = 3*(35) + 1 = 105 + 1 = 106 .
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The answer is: m∡2 = 106° .
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Does this value make sense? Let us check our work:
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If "m∡2 + m∡3 = 180 ;
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then, " m∡3 = (180 − m∡2) = (180 −106) = 74 ;
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Does m∡3 = 174 ??
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We are given: "m∡3 = 2x + 4" ;
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Let us plug in our solved value, "35", for "x" in this expression;
to see if " m∡3 = 74 " ;
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m∡3 = 2x + 4 = 2*(35) + 4 = 70 + 4 = 74?? Yes!
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