Which confirms that δabc∼δa'b'c by the aa criterion?

In similar triangles ∠A=∠A', ∠B=∠B', ∠C=∠C'.

∠A=∠A', 4x-4=51-x,  5x = 55, x=11
∠A=∠A', 4*11-4=51-11, 40=40, ∠A=∠A'= 40⁰

∠B=∠B', 6x - 1 = 4x + 21, 6*11 -1 = 4*11 + 21, 65 = 65, ∠B=∠B'=65
∠C=∠C', 8x - 13 = 6x + 9, 8*11 -13 = 6*11 +9, 75 = 75, ∠C=∠C' = 75

 ∠B=∠B'=65, ∠C=∠C' = 75
So, answer is D.

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