The measure of angle R is 2π ⁄ 3 radians. The measure of angle T is 5π ⁄ 12 radians greater than the measure of angle R. What is the measure of angle T, in degrees?

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Accepted Answer

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

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