The angle in the dilated figure is the same as the original angle in each case, a fact that should be confirmed by the way the answer choices are shown.
∠A = ∠A'
... 4x -4 = 51 -x
... 5x = 55
... x = 11
∠A = 4·11 -4 = 40 . . . . . . doesn't match any offered choice
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∠B = ∠B'
... 6x -1 = 4x +21
... 2x = 22
... x = 11
... ∠B = 6·11 -1
... ∠B = ∠B' = 65 . . . . . matches selection D)
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∠C = ∠C'
... 8x -13 = 6x +9
... 2x = 22
... x = 11
... ∠C = 6·11 +9 = 75
... ∠C = ∠C' = 75 . . . . . matches selection D)