Let $R$ be a reduced root system. ($R$ is a finite set spanning $V$, $\alpha \in R \rightarrow -k\alpha \in R$ iff $k=1$, $s_{\alpha}(R)=R$, $s_{\alpha}(\beta)-\beta=k\alpha$ whit $k$ integer).
Fulton Harris at page 321 states that the angle between two roots must be the same for any pair of adjacent roots in a two dimensional root system, but I am having problem proving this. Any help?