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Geometry and Trigonometry / Circles Difficulty: Medium

The measure of angle $R$ is $StartFraction 2 pi Over 3 EndFraction$ radians. The measure of angle $T$ is $StartFraction 5 pi Over 12 EndFraction$ radians greater than the measure of angle $R$ . What is the measure of angle $T$ , in degrees?

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Explanation

Choice C is correct. It’s given that the measure of angle $R$ is $StartFraction 2 pi Over 3 EndFraction$ radians, and the measure of angle $T$ is $StartFraction 5 pi Over 12 EndFraction$ radians greater than the measure of angle $R$ . Therefore, the measure of angle $T$ is equal to $\frac{2 π}{3} + \frac{5 π}{12}$ radians. Multiplying $StartFraction 2 pi Over 3 EndFraction$ by $\frac{4}{4}$ to get a common denominator with $StartFraction 5 pi Over 12 EndFraction$ yields $StartFraction 8 pi Over 12 EndFraction$ . Therefore, $\frac{2 π}{3} + \frac{5 π}{12}$ is equivalent to $\frac{8 π}{12} + \frac{5 π}{12}$ , or $StartFraction 13 pi Over 12 EndFraction$ . Therefore, the measure of angle $T$ is $StartFraction 13 pi Over 12 EndFraction$ radians. The measure of angle $T$ , in degrees, can be found by multiplying its measure, in radians, by $StartFraction 180 Over pi EndFraction$ . This yields $\frac{13 π}{12} \times \frac{180}{π}$ , which is equivalent to $195$ degrees. Therefore, the measure of angle $T$ is $195$ degrees.

Choice A is incorrect. This is the number of degrees that the measure of angle $T$ is greater than the measure of angle $R$ .

Choice B is incorrect. This is the measure of angle $R$ , in degrees.

Choice D is incorrect and may result from conceptual or calculation errors.