The correct answer is: [B]: " ∠C ≅ ∠F " . ______________________________________________________ Note: We are given that:
"I<span>n △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</span>°<span> (by definition); we can solve for: m</span>∠C ;
m∠C = 180 − (38 + 67) = 180 <span>− 105 = 75 .
</span>m∠C = 75° ; ________________________________________________________ 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° . __________________________________________________ So, let us consider the answer choices given: __________________________________________________ Choice [A]: "m∠F = 67° " ; is incorrect. We know that "<span>m∠F = 75° " . __________________________________________________ Choice [B]: " </span>∠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 . ___________________________________________________ Choice [C]: "<span>m∠C = 75° only" ; is incorrect. While it is correct that: "m</span><span>∠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. ___________________________________________________ Choice [D]: "</span><span>∠C is not necessarily congruent to ∠F. " ; This answer choice is INCORRECT; as explained in Answer choice: [B]: (see above). ___________________________________________________ Choice [E]: "</span>It is not possible to determine m∠F." ; This answer choice is INCORRECT. We know that " m∠F = 75° " . ___________________________________________________ Choice [F]: " <span>It is not possible to determine m∠C." ; This answer choice is INCORRECT. We know that " m</span>∠C = 75° " . ___________________________________________________ The correct answer is: [B]: " <span>∠C ≅ ∠F " . ___________________________________________________</span>