The sum of all interior plus all exterior angles of a convex hexagon is:

The sum of all interior plus all exterior angles of a convex hexagon is:
  1. $720^{\circ}$
  2. $1080^{\circ}$
  3. $1260^{\circ}$
  4. $1440^{\circ}$

Solution

Interior sum $= 720^{\circ}$, exterior sum $= 360^{\circ}$. Total $= 720 + 360 = 1080^{\circ}$. (This also equals $n \cdot 180^{\circ} = 6 \cdot 180$.)

Asked in: IMO

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