The vertex model for epithelia models the apical surface of a tissue by a tiling, with polygons representing cells and edges representing cell-cell junctions. The mechanics are described by an energy governed by deviations from a target area and target perimeter for each cell. It has been shown that the target perimeter p0 governs a solid-to-fluid phase transition: when the target perimeter is low, there is an energy barrier to rearrangement, and when it is high, cells may rearrange for free and the tissue can flow like a liquid. One simplification often made is modeling junctions using straight edges. However, the Young-Laplace equation states that interfaces should be circular arcs, with the curvature being equal to the pressure difference between the neighboring cells divided by the interfacial tension. Here, we investigate how including curved edges alters the mechanical properties of the vertex model and the equilibrium shape of individual cells. Importantly, we show how curved edges shift the solid-to-fluid transition point, from p0=3.81 to p0=3.73, allowing tissues to fluidize sooner than in the traditional model with straight edges.