Let $l_1$ and $l_2$ be two lines intersecting at an angle of $\pi/n$ on $\mathbb{R}^2$. Let $r_1$ and $r_2$ denote the reflection by $l_1$ and $l_2$ respectively. I am to show that $r_1$ and $r_2$ generate a Dihedral group $D_n$.
First I claim that $D_n$ can be generated by a reflection $r$ about a line and rotation by angle $2\pi/n$, $\rho_{2\pi/n}$, because reflection by any other line intersecting at an angle of $2\pi m/n$ can be obtained by first applying $\rho_{2\pi/n}$ $m$ times, followed by $r$, and then followed by $\rho_{2\pi/n}^{-1}$ $m$ times.
Then I deduce from drawing and basic geometry that $$r_1 r_2 = \rho_{2\pi/n}$$
Therefore $r_1$ and $r_2$ generates a Dihedral group $D_n$.
I am not sure if my answer is correct or rigorous enough.
I would add more information about what exactly the group you're generating is and its structure. In particular, the transformations should have the structure of D_n. In this case, the group elements are the transformations, and group operation is composition.
Keep in mind the group is more than just its elements -- you are showing the elements have a particular structure.