Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 113: 61a

$13\frac{1}{3}^{\circ}$, $\frac{2\pi}{27}$ radians

Since a complete circle represents $360^{\circ}$, the measure of each central angle can be found by dividing $360^{\circ}$ by the number of spokes i.e. $27$: Each central angle=$\frac{360^{\circ}}{27}=13\frac{1}{3}^{\circ}$ Since a complete circle represents $2\pi$ radians, the measure of each central angle can be found by dividing $2\pi$ radians by the number of spokes i.e. $27$: Each central angle=$\frac{2\pi}{27}$ radians