To convert an angle from degrees to radians, you use the conversion factor [tex]\( \frac{\pi}{180} \)[/tex]. This means you multiply the degree measure by [tex]\( \frac{\pi}{180} \)[/tex].
Given the angle [tex]\( 50^\circ \)[/tex]:
1. Start by writing down the conversion formula:
[tex]\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\][/tex]
2. Substitute [tex]\( 50 \)[/tex] for the degree measure:
[tex]\[
\text{radians} = 50 \times \frac{\pi}{180}
\][/tex]
3. Simplify the fraction:
[tex]\[
\text{radians} = \frac{50 \pi}{180}
\][/tex]
4. Simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 10:
[tex]\[
\frac{50 \pi}{180} = \frac{5 \pi}{18}
\][/tex]
So, [tex]\( 50^\circ \)[/tex] is equal to [tex]\( \frac{5}{18} \pi \)[/tex] radians.
Hence, the correct answer is:
[tex]\[
\boxed{\frac{5}{18} \pi}
\][/tex]
