a. To find r, we need to use the given arc length of 20 cm and the angle of 50∘ that creates the arc. The arc length, s, of a circle is given by the formula \(\displaystyle{s}=θ{360}∘{\left({2}π{r}\right)}\) where θ is the angle that creates the arc and r is the radius of the circle. We know the arc length is s=20 cm and the angle is θ=50∘. Therefore:

\(\displaystyle{s}={\left(

\(\displaystyle{s}={\left(