Question

¿cuál es la medida en grados de un ángulo que mide \\(\frac{3\pi}{4}\\) radianes?\
\\(\bigcirc\\) a. \\(60^{\circ}\\)\
\\(\bigcirc\\) b. \\(90^{\circ}\\)\
\\(\bigcirc\\) c. \\(135^{\circ}\\)\
\\(\bigcirc\\) d. \\(180^{\circ}\\)

Explanation:

Step1: Use radian-degree conversion

We know $\pi$ radians = $180^\circ$, so the conversion formula is $\text{degrees} = \text{radians} \times \frac{180^\circ}{\pi}$

Step2: Substitute the given radian value

$$\frac{3\pi}{4} \times \frac{180^\circ}{\pi}$$

Step3: Simplify the expression

Cancel $\pi$, then calculate $\frac{3 \times 180^\circ}{4} = 3 \times 45^\circ = 135^\circ$

Answer:

C. $135^\circ$