Every set of 10 points in the plane contains a 4-subset whose angles all lie outside the interval 90° ± 4°, yet there exist 10-point sets in which every 4-subset has at least one angle inside 90° ± 9.292°.
Elekes, A note on a problem of Erd˝ os on right angles.Discrete Math.309 (2009), 5253–5254
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The deviation from right angles in $k$-subsets of points in the plane
Every set of 10 points in the plane contains a 4-subset whose angles all lie outside the interval 90° ± 4°, yet there exist 10-point sets in which every 4-subset has at least one angle inside 90° ± 9.292°.