Question

the measure of angle r is \\(\frac{2pi}{3}\\) radians. the measure of angle t is \\(\frac{5pi}{12}\\) radians greater than the measure of angle r. what is the measure of angle t, in degrees? a) 75 b) 120 c) 195 d) 390

Explanation:

Step1: Calculate angle T in radians

Add angle R and $\frac{5\pi}{12}$:
$$T = \frac{2\pi}{3} + \frac{5\pi}{12}$$
Convert $\frac{2\pi}{3}$ to $\frac{8\pi}{12}$ to get a common denominator:
$$T = \frac{8\pi}{12} + \frac{5\pi}{12} = \frac{13\pi}{12}$$

Step2: Convert radians to degrees

Use the conversion factor $\frac{180^\circ}{\pi}$:
$$T = \frac{13\pi}{12} \times \frac{180^\circ}{\pi}$$

Step3: Simplify the expression

Cancel $\pi$, then calculate $\frac{13 \times 180}{12}$:
$$T = 13 \times 15 = 195^\circ$$

Answer:

C) 195