The answer is:  " ∠= 124°  " .
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Step-by-step explanation:
We are asked to find: "m" (the "measurement");
specifically, " ∠"  ;
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 →  which, from the diagram given:
     is represented by "(11x + 14)" .
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 → If we can solve for the value of "x" ; then we can solve for:
  "(11x + 14)" ;  i.e. " ∠" .
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Let us consider " ∡ " ;
  → which is the "supplementary angle" to:  " ∡ " :
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That is:  " ∠+ ∠ =  180° " .
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Note:  By definition, "supplementary angles" add up to: "180° " ;
               → even if multiple angles are involved.
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Note:  "∡ " and " ∡ " —
            together — form a "straight line" ;
            →  which means that the 2 (two) angles are          Â
              "supplementary" ; and:
            →  which means that the:  sum of the measurements of            Â
               the  " 2 (two) angles " —equal:  " 180° .
  {Note:  by "forming a straight line" ;  for this purpose, this criterion also is satisfied by forming a "straight line on a line segment" —even if that "line segment" is actually:
  1)  an actual "line segment" ;  or: Â
  2)  a portion of a "line segment" ;
  3)  a "line segment" that is actual part of a "true geometry line" ; or
                                  "[geometric] ray".}
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So: We have:
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→  " ∠ +  ∠ = 180 " ;
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Given:  " ∠= (11x + 14) " ;
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Plug in this value for:  " ∠" ;
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→  " (11x + 14)  +  ∠ = 180 " ;  Solve for: " ∠" :
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→  Subtract:  "(11x + 14)" ; from Each Side of the equation:
  to isolate:  " ∠" ;  on one side of the equation;
   & to solve for:  " ∠" ; in terms of "x" :
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→  " (11x + 14)  +  ∠ − (11x + 14) = 180 − (11x + 14) " ;
Note: Â On the "left-hand side" of the equation:
 The:  "(11x + 14)" 's  cancel out to "0" ;
  {since:  (11x + 14)  −  (11x + 14) = 0 ;
        → {i.e. any value, minus that same value, equals: "zero".}.
 →  And we have:  " ∠=  180 − (11x + 14) " ;
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Note:  " 180 − (11x + 14) " ;
 ↔  Treat as:
     " 180 − 1 (11x + 14) " ;
       → {since multiplying by "1" results in the same value.}.
Consider the following portion:
    "  − 1 (11x + 14) " ;
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Note the "distributive property" of multiplication:
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      →   ;
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Likewise:  " − 1 (11x + 14)  = (-1*11x) + (-1 *14) ;
                  = (-11x)  + ( -14) ' Â
                  =  - 11x − 14 ; Â
    {Since:  "Adding a negative" results in the same value as:
          "Subtracting a positive."}.
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Now, bring down the "180" ; and rewrite the expression:
   →  " 180 − 11x − 14  " ;
     →  Combine the "like terms" :
         + 180 − 14  =  + 166 ;
Rewrite the expression as:
   →  " 166 − 11x " ;
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Now, we can rewrite the entire equation:
 " ∠ =  166 − 11x " ;
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Now, consider the triangle:  ΔQRP ;
with its 3 (three) sides—as shown in the image attached:
Note:
By definition:
All triangles:
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1) have 3 (three) sides;
2) have 3 (three) angles; Â and:
3) have angles in which the sum of the measurements of those angles add up to 180°.
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So:  For ΔQRP ; which is shown in the image attached:
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Let us consider the measurements of Each of the 3 (three) angles of that triangle:
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1)  m∡Q = "(5x + 18)" ; (given);
2)  m∡R  = " 56 " ; (given) ;
3)  m∡P —[within the triangle] = "(166 − 11x)" ; (calculated above}.
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We want to find the value for "x" ;
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So:  since all triangles, by definition; have 3 (three) angles with measurements that add up to 180° ;
 → Let us add up the measurements of each of the 3 (three) angles of:
 ΔQRP ;  and make an equation by setting this sum "equal to:  180 ."
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  →  " m∡Q  + m∡R + m∡P = 180 " ;
  →  (5x + 18) + 56) + (166 - 11x) = 180 ;
  →  5x + 18 + 56 + 166 − 11x = 180 ;
On the "left-hand side" of the equation:
 Combine the "like terms" to simplify further:
     +5x − 11x  =  − 6x ;
     + 18 + 56 + 155 = 240 ;
And rewrite the equation:
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 - 6x + 240 − 240 = 180 − 240 ;
to get:
 - 6x  =  - 60 ; Â
Now, divide Each side of the equation by: Â "( -6)" ;
 to isolate: "x" on one side of the equation;
  & to solve for "x" ;
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  - 6x / 6   =  - 60 / -6  ;
to get:
   "  x  = 10 " .
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Now, the question asks for:
" the measurement for angle TPQ ";
 → {that is;  " ∠" } ;
 →  which is:  " (11x + 14) " ;
Since we know that: Â " x = 10 " ;
 We can plug in our "10" as our value for "x" ; and solve accordingly:
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 →  " ∠= (11x + 14) =  (11*10) + 14 = 110 + 14 = 124 .
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The answer is:  " ∠ =  124°  " .  Â
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Hope this answer—and explanation—is helpful!
 Best wishes!
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