In the xy-plane above, points P, Q, R, and T lie on the circle with center O. The degree measures of angles and
are each 30°. What is the radian measure of angle
?
Correct answer: C
Explanation
Choice C is correct. Because points T, O, and P all lie on the x-axis, they form a line. Since the angles on a line add up to , and it’s given that angles POQ and ROT each measure
, it follows that the measure of angle QOR is
. Since the arc of a complete circle is
or
radians, a proportion can be set up to convert the measure of angle QOR from degrees to radians:
, where x is the radian measure of angle QOR. Multiplying each side of the proportion by
gives
. Solving for x gives
, or
.
Choice A is incorrect and may result from subtracting only angle POQ from to get a value of
and then finding the radian measure equivalent to that value. Choice B is incorrect and may result from a calculation error. Choice D is incorrect and may result from calculating the sum of the angle measures, in radians, of angles POQ and ROT.
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