SAT Math Multiple Choice Question 975: Answer and Explanation

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Question: 975


The semicircle shown has its center at point Q. If the measure of the central angle of the shaded sector is 160 degrees, what is the value of x in radians?

  • A. π20
  • B. π12
  • C. π9
  • D. π6

Correct Answer: C



Difficulty: Medium

Category: Additional Topics in Math / Geometry

Strategic Advice: In most cases, it is easier to carry out calculations in degrees, and then convert your answer to radians.

Getting to the Answer: There are 180° in a semicircle (half of 360°). If the central angle of the shaded sector is 160°, then the value of x, in degrees, is 180° - 160° = 20°. To convert this to radians, multiply by the conversion factor that has degrees in the denominator:, which is (C).

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