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No, not in plane (Euclidean) geometry. But on the surface of a sphere, a quadrilateral bounded by 2 sets of great circles [one set has its intersecting points at what would be the 'poles', and the other set has its intersecting points on opposite sides of what would be the 'equator'] will have 4 acute interior angles.

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Q: Is it possible for a quadrilateral to have 4 acute angles?
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