$ABCDE$ is a regular pentagon inscribed in $⊙O$, meaning that each of its five vertices just touches the circle.  

1. Draw a diagram of $ABCDE$ and $⊙O$ on your paper.

   Answer (a):

   

2. Find $m∠EDC$. How did you find your answer?

   Step 1(b):

   $\text{sum of interior angles}=180(n-2)\\ \qquad \qquad \qquad \qquad \quad \ =180(5-2)$
   $\text{sum of interior angles}= 540^{\large\circ}$

   Step 2(b):

   $\angle EDC=\frac{1}{5}\text{(sum of interior angles)}$

   Answer (b):

   $\angle EDC=\frac{1}{5}(540)=108^{\large\circ}$

3. Find $m∠BOC$. What relationship did you use?

   Answer (c):

   $\angle BOC=\frac{360^{\large\circ}}{5}=72^{\large\circ}$

4. Find $m\overarc{ E B C }$. Is there more than one way to do this?

   Hint (d):

   How is the inscribed angle related to the intercepted arc?