Question

convert the angle \\(\theta = \frac{133\pi}{72}\\) radians to degrees.
express your answer exactly.
\\(\theta = \\) \\(^{\circ}\\)

Explanation:

State the conversion formula

$$ \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} $$

Substitute the given angle

$$ \theta = \frac{133\pi}{72} \times \frac{180}{\pi} $$

Simplify the expression

$$ \theta = \frac{133 \times 180}{72} = \frac{133 \times 5}{2} = \frac{665}{2} = 332.5 $$

Answer:

Convert the angle \(\theta = \frac{133\pi}{72}\) radians to degrees.
Express your answer exactly.

\(\theta =\) <blank>\(332.5\)</blank>\(^\circ\)