We have shown in the hyperbolic plane, the angle sum of a triangle is less than...

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We have shown in the hyperbolic plane, the angle sum of a triangle is less than 180 (or π) and the angle sum of a convex quadrilateral is less than 360 (or 2π). 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)π ) for all n ≥ 3. We have shown in the hyperbolic plane, the angle sum of a triangle is less than 180 (or π) and the angle sum of a convex quadrilateral is less than 360 (or 2π). 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)π ) for all n ≥ 3.

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To prove that the angle sum of a convex polygon with n sides in the hyperbolic plane is less than n2180 or n 2 for all n 3 we can use mathematical ind... View the full answer