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

Explanation

Choice C is correct. It's given that the measure of angle R is 2π3 radians, and the measure of angle T is π5 / 12 radians greater than the measure of angle R. Therefore, the measure of angle T is equal to 2 5 π π3 12+ radians. Multiplying π23 by 44 to get a common denominator with 5π12 yields π812. Therefore, π π2 53 12+ is equivalent to π π8 512 12+ , or 1312π . Therefore, the measure of angle T is π1312 radians. The measure of angle T , in degrees, can be found by multiplying its measure, in radians, by π180. This yields π π13 18012´, which is equivalent to 195 degrees. Therefore, the measure of angle T is 195 degrees.