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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

The figure above consists of three large, similar, isosceles triangles, AJF, EIG, and FHB. The corresponding legs of the large triangles are parallel, and all of the smaller triangles are also isosceles. What is the value of θ?

A.46
B.67
C.113
D.134

答案和解析

答案：A

解析：

Choice A is correct.
m∠FEI=67°, since it is supplementary to the 113° angle.
Also, m∠GFH=67°, since it is a corresponding angle to ∠FEI. Also, m∠JFE=67°, since all triangles are isosceles.
Next, we see the following.
180°-2*67°=θ
θ=46°
The correct answer is: θ=46°.