Hi Crystal,

The circumference of a circle of radius $r$ cm is $2 \times \pi \times r$ cm. Thus in your case the circumference of your circle is $24 \times \pi$ cm. The 20 cm arc is hence $\large \frac{20}{24 \pi}$ of the circumference of the circle. Using the symmetry of the circle you can see that the central angle which makes the arc is $\large \frac{20}{24 \pi}$ of the $360^o$ which forms the central arc of the entire circle.

Penny