Graph Coloring · Superchallenge problem

Let $G$ be the $7$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}6\text{-}7\text{-}1$ with one extra pendant vertex $8$ attached to vertex $1$ ($8$ edges on $8$ vertices). Find $\chi(G) + \chi'(G)$.