Angles between two geodesics

Question

I've just started differential geometry with do carmo textbook. I get to geodesic concept and its properties and can't understand a simple fact. Why the external angle between two geodesic can't achieve $\pi$ value or equivalently at a corner with two geodesic segment the external angle $|\theta| < \pi$ and $\theta \neq\pi$? My question is why this external angle can't be exactly $\pi$. (External angle means the angles between their tangent line)