Question

If in △ABC, m∠A=38° and ​m∠B=67°, and in △DEF, m∠D=38° and m∠E=67°, which statements are true?

Answer 1

The correct answer is:  [B]:  " ∠C ≅ ∠F " .
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Note:  We are given that:  

"In △ABC, m∠A=38° and m∠B=67 " .

Since a triangle has three (3) angles (by definition) ; and since all 3 angles in any triangle must add up to 180° (by definition);  we can solve for:
m∠C ;   

   m∠C = 180 − (38 + 67) =  180 − 105  = 75 .

m∠C = 75° ;
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Likewise, given △DEF, m∠D=38° and m∠E=67 ; we find m∠F as follows:

m∠F = 180 - (38 + 67) =  180 − 105  = 75 .

m∠F  = 75° .
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 So, let us consider the answer choices given:
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  Choice [A]:  "m∠F = 67° "  ; is incorrect.  We know that "m∠F = 75° " .
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  Choice [B]:  " ∠C ≅ ∠F " is correct.  We know that ΔABC ≅ ΔDEF ; and that;

m∠A = m∠D = 38° ; and that:  m∠B = m∠E = 67° ; and that: 
 m∠C = m∠F = 75° ;  and as such:

  ∠A ≅ D ; and ∠B ≅ ∠E ; and ∠C ≅ ∠F .
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  Choice [C]:   "m∠C = 75° only" ; is incorrect.  While it is correct that:  
                       "m∠C = 75° " ;  this answer choice is INCORRECT; since this answer choice is not the ONLY answer choice provided that holds true.  In fact, we have already determined that answer choice: [B] (see above) is a correct statement.
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 Choice [D]:  "∠C is not necessarily congruent to ∠F. " ;  This answer choice is INCORRECT; as explained in Answer choice: [B]: (see above).
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Choice  [E]:  "It is not possible to determine m∠F." ;  This answer choice is INCORRECT.  We know that " m∠F = 75° " .
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Choice  [F]: " It is not possible to determine m∠C." ; This answer choice is 
INCORRECT.  We know that " m∠C = 75° " .
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The correct answer is:  [B]:  " ∠C ≅ ∠F " .
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