To convert an angle from degrees to radians, we use the fact that [tex]\(180\)[/tex] degrees is equivalent to [tex]\(\pi\)[/tex] radians.
Steps for conversion:
1. Identify the given angle in degrees:
[tex]\[
\text{Angle in degrees} = 20^\circ
\][/tex]
2. Use the conversion formula where 1 degree is [tex]\(\frac{\pi}{180}\)[/tex] radians:
[tex]\[
\text{Angle in radians} = \left(\text{Angle in degrees}\right) \times \left(\frac{\pi}{180}\right)
\][/tex]
3. Substitute the given angle into the formula:
[tex]\[
20^\circ \times \frac{\pi}{180}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{20\pi}{180}
\][/tex]
5. Reduce the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. In this case, 20 and 180 are both divisible by 20:
[tex]\[
\frac{20 \div 20}{180 \div 20} = \frac{1}{9}
\][/tex]
6. Thus, the fraction simplifies to:
[tex]\[
\frac{\pi}{9}
\][/tex]
So, the radian measure of a [tex]\(20^\circ\)[/tex] angle is:
[tex]\(\boxed{\frac{\pi}{9}}\)[/tex]
