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).