SSAT Math Question 662: Answer and Explanation
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Question: 662
6. 
What is the value of x ?
- A. 360
- B. 100
- C. 97
- D. 67
Correct Answer: D
Explanation:
Notice that the four intersecting lines form a quadrilateral. All quadrilaterals contain 360o, so keep a tally of the vertices and find the missing angle. 80o is already provided, so 360o - 80o = 280o. All straight lines add up to 180o, so use the exterior angles to find the interior angles. If one of the exterior angles is 75o, the supplementary angle must be 105o. Subtract this from 280o to find that 280o - 105o = 175o. The other exterior angle, 108o, is opposite the interior vertex. Since opposite angles are equal, the interior vertex must also be 108o. Subtract this from the current total to find that 175o - 108o = 67o. The missing angle is 67o. The correct answer is (D).