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integer angles in convex polygon , whose degrees are divisible by 36

Source: 2008 Swedish Mathematical Competition p4

April 27, 2021
anglesgeometrycombinatorial geometry

Problem Statement

A convex nn-side polygon has angles v1,v2,…,vnv_1,v_2,\dots,v_n (in degrees), where all vkv_k (k=1,2,…,nk = 1,2,\dots,n) are positive integers divisible by 3636. (a) Determine the largest nn for which this is possible. (b) Show that if n>5n>5, two of the sides of the nn-polygon must be parallel.
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