Question

For ΔABC, ∠A = 3x - 8, ∠B = 5x - 6, and ∠C = 4x + 2. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A' = 2x + 8, ∠B' = 90 - x, and ∠C' = 5x - 14, which confirms that ΔABC∼ΔA'B'C by the AA criterion? A) ∠A = ∠A' = 37° and ∠B = ∠B' = 69° B) ∠A = ∠A' = 22° and ∠C = ∠C' = 42° C) ∠B = ∠B' = 37° and ∠C = ∠C' = 33° D) ∠B = ∠B' = 74° and ∠C = ∠C' = 66°

Answer 1

The sum of angles in a triangle add up to 180 degrees
Therefore, for Δ ABC;
3x-8+5x-6+4x+2 = 180
12x = 192
x = 16
Hence ∠A = 40, ∠B = 74 and ∠C = 66
For the ΔA'B'C'
2x+8+90-x+5x-14 =180
6x + 84 =180
6x = 96
x = 16
Hence; ∠A' = 40, ∠B' =74, and ∠C' = 66
Therefore, the correct answer is D. ∠B=∠B'=74° and ∠C=∠C'=66°