Fourier transform (FT) spectroscopy is a versatile technique for studying the infrared (IR) optical response of solid-, liquid-, and gas-phase samples. In standard Fourier transform infrared (FT-IR) spectrometers, a light beam passing through a Michelson interferometer is focused onto a sample with condenser optics. This design enables us to examine relatively small samples, but the large solid angle of the focused infrared beam makes it difficult to analyze angle-dependent characteristics. Here, we design and construct a high-precision angle-resolved reflection setup compatible with a commercial FT-IR spectrometer. Our setup converts the focused beam into an achromatically collimated beam with an angle dispersion as high as 0.25°. The setup also permits us to scan the incident angle over ∼8° across zero (normal incidence). The beam diameter can be reduced to ∼1 mm, which is limited by the sensitivity of an HgCdTe detector. The small-footprint apparatus is easily installed in an FT-IR sample compartment. As a demonstration of the capability of our reflection setup, we measure the angle-dependent mid-infrared reflectance of two-dimensional photonic crystal slabs and determine the in-plane dispersion relation in the vicinity of the Γ point in momentum space. We observe the formation of photonic Dirac cones, i.e., linear dispersions with an accidental degeneracy at Γ, in an ideally designed sample. Our apparatus is useful for characterizing various systems that have a strong in-plane anisotropy, including photonic crystal waveguides, plasmonic metasurfaces, and molecular crystalline films.