We can use the distance formula to determine the side lengths of DEF.
D (3, -1)
E (7, -4)
F (4, -4)
DE --> √((7 - 3)^2 + (-4 - (-1))^2) = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5
DF --> √((4 - 3)^2 + (-4 - (-1))^2) = √(1^2 + (-3)^2) = √(1 + 9) = √10 ≈ 3.2
EF --> √((7 - 4)^2 + (-4 - (-4)^2) = √(3^2 + 0^2) = √9 = 3
Notice DEF is congruent to ABC because due to SSS (side-side-side) congruency; DE = AB, DF = AC, EF = BC. Because DEF and ABC are congruent, DEF and ABC must have congruent angles.
angleBAC = angleEDF = 34.7 degrees
angleACB = angleDFE = 108.4 degrees
angleCBA = angleFED = 36.9 degrees