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Textbook Expert
Textbook ExpertVerified Tutor
5 Dec 2021

Given information

A sphere is given.

 

 

 

 

Step-by-step explanation

Step 1.

All lines, lying on the sphere are curved lines and the triangles so formed are called spherical triangles.

According to the Euclidean postulate:

Spherical geometry violates the parallel postulate and there exists a triangle such that the sum of the angles of a triangle on a sphere is  , where   is the fraction of the sphere's surface that is enclosed by the triangle

Hence for the maximum sum of angles, we can consider the half portion of sphere being enclosed to form triangle , since it is the maximum limit of fraction of sphere to be considered( triangle requires 3 curved lines)

Hence  

then max sum of angles in spherical triangle is :

 

Hence the maximum sum of angles of a triangle enclosed in sphere is  

3D-View is shown below:

( Graphed using GeoGebra)

 

 

 

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