Question

For ΔABC, ∠A = 2x - 2, ∠B = 2x + 2, and ∠C = 5x. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A' = 58 - x, ∠B' = 3x - 18, and ∠C' = 120 - x, which confirms that ΔABC∼ΔA'B'C by the AA criterion?
A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°

B) ∠A = ∠A' = 19° and ∠C = ∠C' = 21°

C) ∠B = ∠B' = 18° and ∠C = ∠C' = 50°

D) ∠B = ∠B' = 32° and ∠C = ∠C' = 75°

Answer 1

Answer:

A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°

Explanation:

The sum of angles in ∆ABC is 180°, so ...

... (2x -2) + (2x +2) + (5x) = 180

... 9x = 180

... x = 20

and the angles of ∆ABC are ∠A = 38°, ∠B = 42°, ∠C = 100°.

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The sum of angles of ∆A'B'C' is 180°, so ...

... (58 -x) +(3x -18) +(120 -x) = 180

... x +160 = 180

... x = 20

and ∠A' = 38°, ∠B' = 42°, ∠C' = 100°.

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The values of angle measures of ∆ABC match those of ∆A'B'C', so we can conclude ...

... A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°