The interior angles of a convex polygon add up to three times the total of its exterior angles, one exterior angle being taken at each vertex. How many sides has the polygon?

One exterior angle at each vertex of any convex polygon always totals 360°, however many sides it has. So the interior angles must total $3\times 360$° = 1080°. The interior sum is $(n-2)\times 180$°, so $(n-2)\times 180=1080$, giving $n-2=6$ and $n=8$ — an octagon. The usual slip is to imagine the exterior total growing with $n$; it stays fixed at 360°.