ISEE Mathematics Achievement Question 283: Answer and Explanation

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Question: 283

13.

What is the value of x ?

  • A. 360
  • B. 100
  • C. 97
  • D. 67

Correct Answer: D

Explanation:

D Notice that the four intersecting lines form a quadrilateral. All quadrilaterals contain 360°, so keep a tally of the vertices and find the missing angle. 80° is already provided, so 360° - 80° = 280°. All straight lines add up to 180°, so use the exterior angles to find the interior angles. If one of the exterior angles is 75°, the supplementary angle must be 105°. Subtract this from 280° to find that 280° - 105° = 175°. The other exterior angle, 108°, is opposite the interior vertex. Since opposite angles are equal, the interior vertex must also be 108°. Subtract this from the current total to find that 175° - 108° = 67°. The missing angle is 67°. The correct answer is (D).

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