Question: We have shown in the hyperbolic plane, the angle sum of a triangle is less than 180 (or ) and the angle sum of

We have shown in the hyperbolic plane, the angle sum of a triangle is less than 180 (or ) and the angle sum of a convex quadrilateral is less than 360 (or 2). Prove by induction that the angle sum of a convex polygon with n sides in the hyperbolic plane is less than (n 2)180 (or (n 2) ) for all n 3.

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