We have two responses for you

Makayla,

Since the title of your problem is 'problem solving', I think the key is to look at your reasoning.

I suspect that you drew an example, and found that your example had 10 vertices.
This is certainly a good start. If you imagine shifting them around a bit, or making some longer and shorter - does the number of vertices change? This is also part of your reasoning.

You can back up the reasoning in a couple of ways: is 10 a magic number?
Is there a pattern that works for three sides, four sides, five sides? This pattern gives some back-up for your reasoning. (Good problem solving works for more than one problem!)

If you imagine walking around the shape: edge vertex edge vertex .... because it is CLOSED (have to use that somewhere) you can write out a 'cycle' with 10 edges which is general enough that you can just 'count' the vertices.

Hope this helps.

Walter Whiteley

You are right, Makayla!

In a closed figure, each side attaches to two vertices and each vertex joins two sides, so it makes sense that the number of sides and vertices is the same.

Stephen.