Does $\exists$ on the hyperbolic plane, a convex quadrilateral $Q$ and a convex pentagon $P$ with the same angle sum? I found this question to be rather interesting.
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If you know about ideal polygon then this is easy because every ideal polygon has angle sum zero.
Hint: a regular quadrilateral can have any value of interior angles between 0 and π/2, and a regular pentagon can have any value of interior angles between 0 and 3π/5.