The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?

learnmgcat May 24, 2024

#1**+1 **

Let's say there are x sides on the polygon.

The number of diagonals can be represented by \( x*(x-1)/2 - x \), meaning we can write the equation

\(2x = x*(x-1)/2 - x\).

Solving for this equation, we find that x = 7, which is a heptagon.

A heptagon has 7 sides and indeed has 14 diagonals!

Thanks! :)

NotThatSmart May 24, 2024