For ΔABC, ∠A = 8x - 10, ∠B = 10x - 40, and ∠C = 3x + 20. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A' = 6x + 10, ∠B' = 70 - x, and ∠C' = 10x 2, which confirms that ΔABC∼ΔA'B'C by the AA criterion? A) ∠A = ∠A' = 70° and ∠B = ∠B' = 60° B) ∠A = ∠A' = 35° and ∠B = ∠B' = 30° C) ∠B = ∠B' = 54° and ∠C = ∠C' = 40° D) ∠A = ∠A' = 76° and ∠C = ∠C' = 53°

Question

Garrett Pace

Mathematics

31 July, 13:00

For ΔABC, ∠A = 8x - 10, ∠B = 10x - 40, and ∠C = 3x + 20. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A' = 6x + 10, ∠B' = 70 - x, and ∠C' = 10x 2, which confirms that ΔABC∼ΔA'B'C by the AA criterion? A) ∠A = ∠A' = 70° and ∠B = ∠B' = 60° B) ∠A = ∠A' = 35° and ∠B = ∠B' = 30° C) ∠B = ∠B' = 54° and ∠C = ∠C' = 40° D) ∠A = ∠A' = 76° and ∠C = ∠C' = 53°

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Answers (1)

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Hana Benton · Answer 1

If the triangles ABC and A'B'C' are similar, then

angle A = angle A'

8x-10 = 6x+10

8x-6x = 10+10

2x = 20

x = 20/2

x = 10

So angle A is

angle A = 8x-10

angle A = 8*10-10

angle A = 80-10

angle A = 70

making that the measure of angle A' as well

This is why the answer is choice A