In this short note, we study the distribution of spreads in a point set P ⊆ F d q , which are analogous to angles in Euclidean space. More precisely, we prove that, for any ε > 0, if |P| ≥ (1 + ε)q ⌈d/2⌉ , then P determines a positive proportion of all spreads. We show that these results are tight, in the sense that there exist sets P ⊂ F d q of size |P| = q ⌈d/2⌉ that determine at most one spread.1 Here and throughout, X ≫ Y means that there exists C > 0 such that X ≥ CY .[15] L. A. Vinh, The Erdős-Facolner distance problem in subsets of spheres over finite fields, SIAM Journal on Discrete Mathematics, 25 (2)