SOLUTION: Triangle ABC is rotated 45° counterclockwise about vertex A to obtain triangle XYZ. If the measure of angle ABC is equal to 30°, what is the measure of angle XYZ ? A. 15° B.

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Question 1137531: Triangle ABC is rotated 45° counterclockwise about vertex A to obtain triangle
XYZ. If the measure of angle ABC is equal to 30°, what is the measure of angle XYZ ?
A. 15°
B. 30°
C. 45°
D. 75°
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: B) 30 degrees

Rotations preserve angles, meaning that the angles will not change. Note how B is the second letter of ABC; similarly, Y is the second letter of XYZ. Therefore, angle B = angle X. Or put another way, angle ABC = angle XYZ. Both are 30 degrees.

If you want, you can think of it as rotating the camera rather than rotating the triangle. Triangle ABC will stay put, but the illusion of it moving is what rotates it to triangle XYZ. So this is another way to see how angles are preserved.

note: we don't use the 45 degree rotation info at all. We can rotate any number of degrees and angle ABC = angle XYZ = 30 will stay the same.