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# Geometry

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How many sides would there be in a convex polygon if the sum of all but one of its interior angles is $$4560$$ degrees?

Jan 29, 2022

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.