ISEE Mathematics Achievement Question 278: Answer and Explanation

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Question: 278

8.

If ABCD is a rectangle, what is the value of w + x + y + z ?

  • A. 90
  • B. 150
  • C. 180
  • D. 190

Correct Answer: C

Explanation:

C Notice the three triangles that have been created within the rectangle. Look at the two right triangles that surround the larger (possibly) equilateral triangle in the middle. Since each triangle has a right angle, the other two angles must equal 90° since 180° - 90° = 90°. Thus, in the triangle on the left side that includes side AB, w + x = 90°, and in the triangle on the right side that includes side CD, y + z = 90°. Add all these together to find that 90° + 90° = 180°. The correct answer is (C).

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