Problem 569

$\triangleright$ The total of all arcs is $360^{\circ}$, so each of them is $360^{\circ} / 5=72^{\circ} . \triangleleft$

(The Inscribed Angle Theorem) Let $A, B$ and $C$ be points on a circle with center $O$. Then the angle $B A C$ is equal to half the measure of the arc $B C$, that is, half the angle $B O C$.

The angle $B A C$ is called an inscribed angle subtending the arc $B C$. Then we can say: an inscribed angle is equal to half the arc it subtends.

!