Please answer

Thank you

The correct answers are:

 " (x − 13) ° = 67 ° " ;

 " x = 54 " ;

 " m∠2 = 36° " ;

 " m∠1 = 36° " .

Step-by-step explanation:

Note:  The following "given values/answers" within the attached image:

Specifically:

 (x − 13)° = 72° ; and;

  x = 85° ;

   are: "incorrect"—and are "arbitrarily assigned values"

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.

Let's start by finding the measure of ∠2 ;  that is: " m∠2 " :

To find m∠2:

Note that:  both: "∠2 " ; and the angle that measures "175" with the attached image:

            → both form a straight line—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

So:  To solve for:  "m∠2" :

→  m∠2 = 180 − (125) = 65° ,

Now; to solve for:  " m∠1 " :

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.} ;

→  As such, m∠1 = m∠2 = 65 °.

Now, take either ∠1 or ∠2 ;  

 And combine with angle with the given measurement of 72° ;

 And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;

All three of these angles form a straight line—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

So, 65° + 72° + (x − 13)° = 180° ;

 Let us solve for "x" ; and for "(x − 13)" ;

65 + 72 = 113 ;

→ 113 + (x − 13) = 180 ;

Now, subtract "113" from each side of the equation:

 → 113 + (x − 13) − 113 = 180 − 113 ;

   to get:

          " (x − 13) = 67 " ; →  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" :

      x − 13 + 13 = 67 − 13 ;

      x  = 54 ;

So:  The correct answers are:

 " (x − 13) ° = 67 ° " ;

 " x = 54 " ;

 " m∠2 = 36° " ;

 " m∠1 = 36° " .

Hope these answers—and explanations—are helpful!

  Best wishes!

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