SAT Math Multiple Choice Practice Question 172: Answer and Explanation

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Question: 172

18. In a certain triangle, angle X is twice the size of angle Y, and angle Z is 45 degrees smaller than angle X. Triangle XYZ must be

I.A right triangle

II.An isosceles triangle

III.An equilateral triangle

A. I only
B. II only
C. III only
D. I and II
E. I and III

Correct Answer: D

Explanation:

D. From the instructions, you can write x = 2y and z = x - 45. Because the angles must add up to 180°, you have x + y + z = 180. Substituting gives you 2y + y + x - 45 = 180, and substituting 2y for x again gives you 2y + y + 2y - 45 = 180, which becomes 5y = 225, and y = 45. Therefore, x = 90 and z = 45, which makes the triangle a 45-45-90 triangle — in other words, an isosceles right triangle.

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