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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