Question

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°

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

Answer 2

Answer:

A) ∠A = ∠A' = 70° and ∠B = ∠B' = 60°

Step-by-step explanation:

8x - 10 + 10x - 40 + 3x + 20 = 180

21x - 30 = 180

21x = 210

x = 10

Then, plug in x to find angle measurements.

By the AA criterion, if two of the angles of a triangle are congruent the triangles are similar.