Answer: m∠KNL = 102° .
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Step-by-step explanation:
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m∠KNL = m∠JNM ; Reason: These angles are vertical; and vertical angles are congruent.
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Given:
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m∠KNL = 3 (x + 14) ; and:
m∠JMN = 5x + 2 ;
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And we want to solve for:
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m∠KNL = 3 (x + 14) ;
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And both of these angles are congruent;
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We set this expressions equal to each other; Then solve for "x"; then plug that solved value into "x" into the expression for "m∠KNL" ; to solve for "m∠KNL" ;
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As such:
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3 (x + 14) = 5x + 2 ;
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We expand:
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3 (x + 14) ; Using the "distributive property of multiplication":
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a(b + c) = ab + ac ;
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So, m∠KNL = 3 (x + 14) = (3*x) + (3*14) = 3x + 42 ;
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And rewrite the equation as:
3x + 42 = 5x + 2 ;
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Subtract "3x" and "2" from each side of the equation;
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3x + 42 − 3x − 2 = 5x + 2 − 3x − 2 ;
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to get:
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40 = 2x ;
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↔ 2x = 40 ;
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Now, divide EACH side of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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2x / 2 = 40 / 2 ;
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x = 20 .
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Now, to solve for m∠KNL ;
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From above:
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m∠KNL = 3 (x + 14) = (3*x) + (3*14) = 3x + 42 ;
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→ m∠KNL = 3 (x + 14) = 3x + 42 ;
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Substitute: "20" for "x"
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3*(20 + 14) = 3*34 = 102 ;
Check using "3x + 42" ;
(3*20) + 42 = 60 + 42 = 102.
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Also, m∠JMN = 5x + 2 =? 102? It should.
Let us check, substituting "20" for "x".
5x + 2 =? 102?
(5*20) + 2 =? 102?
(100) + 2 =? 102? Yes!
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So; m∠KNL = 102° .
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