The correct answers are:
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" (x − 13) ° = 53 ° " ;
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" x = 66 " ;
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" m∠2 = 55° " ;
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" m∠1 = 55° " .
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<u>Step-by-step explanation</u>:
Note: The following "given values/answers" within the attached image:
Specifically:
(x − 13)° = 72° ; and;
x = 85° ;
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are: "incorrect"—and are "arbitrarily assigned values"
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The values and expressions given in the attached image, however, are correct/do make sense; and we can use such data to solve the problem.
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Let's start by finding the measure of ∠2 ; that is: " m∠2 " :
To find m∠2:
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Note that: both: "∠2 " ; and the angle that measures "175" with the attached image:
→ both form a <u>straight line</u>—that is;
→ they are "supplementary angles" ;
→ which means they add up to "180° " ;
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So: To solve for: "m∠2" :
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→ m∠2 = 180 − (125) = 55° ,
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Now; to solve for: " m∠1 " :
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Note that ∠1 and ∠2 are vertical angles: which means that they have equal measurements;
{since: vertical angles are congruent; which means that vertical angles are equal.} ;
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→ As such, m∠1 = m∠2 = 55 °.
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Now, take either ∠1 or ∠2 ; (each has the same "measurement"—"55° " ;
And combine with angle with the given measurement of 72° ;
And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;
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All three of these angles form a <u>straight line</u>—that is;
→ they are "supplementary angles" ;
→ which means they add up to "180° " ;
So, 55° + 72° + (x − 13)° = 180° ;
Let us solve for "x" ; and for "(x − 13)" ;
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55 + 72 = 127 ;
→ 127 + (x − 13) = 180 ;
Now, subtract "127" from each side of the equation:
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→ 127 + (x − 13) − 127 = 180 − 127 ;
to get:
" (x − 13) = 53 " ; → which is one of our answers;
Now, to solve for "x" ; we add "13" to Each Side of the equation;
to isolate "x" on one side of the equation; & to solve for "x" :
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x − 13 + 13 = 53 + 13 ;
to get:
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x = 66 ;
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So: The correct answers are:
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" (x − 13) ° = 53 ° " ;
→ Double check by substituting our value of "66" for "x" :
" (66 − 13) =? 53 ? Yes! ;
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" x = 66 " ;
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" m∠2 = 55° " ;
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" m∠1 = 55° " .
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Hope these answers—and explanations—are helpful!
Best wishes!
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