Question

Four students were asked to label angles in pairs of triangles. Their drawings are shown below.


Tatyanna
Triangle A B C. Angle B is 54.3 degrees and angle C is 61.2 degrees. Triangle X Y Z. Angle Z is 64.5 degrees and angle Y is 54.3 degrees.[Not drawn to scale]

Simon
Triangle A B C. Angle A is 63.2 degrees and angle B is 58.4 degrees. Triangle X Y Z. Angle Z is 63.2 degrees and angle Y is 58.4 degrees.[Not drawn to scale]


Anders
Triangle A B C. Angle A is 59.8 degrees and angle B is 60.6 degrees. Triangle X Y Z. Angle X is 59.8 degrees and angle Z is 60.6 degrees.[Not drawn to scale]


Kai
Triangle A B C. Angle B is 60.9 degrees and angle C is 57.7 degrees. Triangle X Y Z. Angle X is 61.4 degrees and angle Z is 57.7 degrees.
[Not drawn to scale]


Which student labeled the triangles such that Triangle A B C is similar to X Y Z?
Tatyanna
Simon
Anders
Kai

Answer 1

Kai.

Reason: For Kai, in triangle ABC B = 60.9°, C = 57.7°, so A = 180 − (60.9 + 57.7) = 61.4°. In triangle XYZ X = 61.4°, Z = 57.7°, so Y = 180 − (61.4 + 57.7) = 60.9°. Thus A = X, B = Y, C = Z, so ABC is similar to XYZ under that vertex correspondence.