Olympiad workbookIOQMProperties of Triangles

Two sides of a regular polygon with n sides, when extended, meet at an angle of 28^ . What is the smallest possible value of n ?

Correct answer

Step-by-step solution

Let the sides extended pass through the vertices which on joining the centre makes angle k(2 ) n aligned & 28+ ( n-2 n ) + 2 k n =360^ & (2 k-2) n =152^ & (k-1) n =76^ & n= (k-1) 45 19 aligned For minimum k=20 and n=45

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