Answer: "12" .__________________________________ " x = 12 " .__________________________________
Explanation:
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The TWO (2) angles:
Angle 1) "(10x − 20)° " ; AND:
Angle 2) " (6x + 8)° " ;
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form a "straight line" ; so by definition; ∡1 and ∡2 are supplementary angles; and as such, m∡1 and m∡2 add up to 180°.
We are asked to solve for "x" .
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10x − 20 + 6x + 8 = 180 ;
Combine the "like terms" on the "left-hand side" of the equation:
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10x + 6x = 16x ;
- 20 + 8 = -12 ;
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Rewrite the equation:
16x − 12 = 180 ;
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Add "12" to both sides of the equation;
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16x − 12 + 12 = 180 + 12 ;
to get:
16x = 192 ;
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Divide EACH SIDE of the equation by "16" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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16x / 16 = 192 ;
x = 12 .
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Let us check our answer, by plugging in "12" for "x" in the original equation:
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→ 10x − 20 + 6x + 8 =? 180 ? ;
→ 10(12) − 20 + 6(12) + 8 =? 180 ? ;
→ 120 − 20 + 72 + 8 = ? 180 ?
→ 120 − 20 = 100 ; 100 + 72 = 172; 172 + 80 =? 180 ? Yes!
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