Question

convert the following angle from degrees to radians. express your answer in simplest form. 255°

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, use the formula: radians = degrees $\times\frac{\pi}{180}$.

Step2: Substitute the given degree value

For $255^{\circ}$, we have $255\times\frac{\pi}{180}$.

Step3: Simplify the fraction

First, find the greatest common divisor (GCD) of 255 and 180. The GCD of 255 and 180 is 15.
Divide both the numerator and denominator by 15: $\frac{255\div15}{180\div15}\times\pi=\frac{17}{12}\pi$.

Answer:

$\frac{17\pi}{12}$