How many sides would there be in a convex polygon if the sum of all but one of its interior angles is \(4560\) degrees?
+2666 The sum of the angles in a convex polygon is \(180\times(s-2)\). If we use \(4560\) as the sum of all the angles in the polygon, we have the equation \(180\times(s-2)=4560\). This simplifies to \(s=82/3\). Now, we have to round up, meaning that there is \(\color{red}\boxed {28}\) sides in the polygon.
