sat-dog

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