The measure of angle R is 2 π 3 radians. The measure of angle T is 5 π 12 radians

Question

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

Accepted Answer

Choice C is correct. It&rsquo;s given that the measure of angle R is 2 3 radians, and the measure of angle T is 5 12 radians greater than the measure of angle R . Therefore, the measure of angle T is equal to 2 3 + 5 12 radians. Multiplying 2 3 by 4 4 to get a common denominator with 5 12 yields 8 12 . Therefore, 2 3 + 5 12 is equivalent to 8 12 + 5 12 , or 13 12 . Therefore, the measure of angle T is 13 12 radians. The measure of angle T , in degrees, can be found by multiplying its measure, in radians, by 180 . This yields 13 12 /mo> 180 , 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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