Answer: " x = 31 " .
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Explanation:
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If the two lines that are shown in the figure: "line a" and "line b" ; are parallel;{ that is; if " a∥b " } :
{ that is; if " a∥b " } :
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The following would be true:
1) "∠2 & ∠8 " would be equal; since they are "alternate exterior angles".
2) "∠1 & ∠7 " would be equal; since they are "alternate exterior angles".
3) "∠1 & ∠3" would be equal; since they are "vertical angles".
4) "∠5 & ∠7 would be equal; since they are "vertical angles".
5) "∠8 & ∠6 would be equal; since they are "vertical angles".
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So, if " a∥b " ; then:
" m∠1 = m∠3 = m∠5 = m∠7 " .
and: " m∠2 = m∠4 = m∠6 = m∠8 " ;
and: " m∠6 + m∠3 = 180 " ;
since: "m∠3 = m∠7 " ;
and: "∠5 & ∠7" are "supplementary angles" ; which, by definition, add up to 180.
Also, look at "∠2 and ∠3" . These are "supplementary angles" , which, by definition, add up to 180.
We know that "m∠2 = m∠6" ; So: " m∠2 + m∠3 = m∠6 + m∠3 = 180 ".
Given "m∠3 + m∠6 = 180" ;
and given: "m∠3 = 2x + 15" ;
and given: "m∠6 = 3x + 10" ;
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→ 2x + 15 + 3x + 10 = 180 ; Solve for "x" ;
→ 2x + 3x = 5x ;
→ 10 + 15 = 25 ;
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→ 5x + 25 = 180 ;
Subtract "25" from each side of the equation:
→ 5x + 25 − 25 = 180 − 25 ;
to get:
→ 5x = 155 ;
Divide each side of the equation by "5" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 5x / 5 = 155 / 5 ;
to get:
→ " x = 31 " .
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