Do octagons have 10 sides?
No, octagons have only 8 sides. Here's a tip to help you to remember: the root of the word octagon is 'octo' which means 'eight'. An octopus has 8 legs and an octagon has 8 sides.
A teacher has 60 pentagons and octagons totaling 354 sides. How many of each pentagon and octagons does she have?
No it does not tessellate you have to pentagons in order for it to tessellate. * * * * * It is not at all clear what "have to pentagons" has to do with this. No polygon with 7 or more sides will tessellate. Octagons will tessellate if mixed with squares but that is not "proper" tessellation since it involved more than one shape.