What is a figure with sides made by line segments that meet to form angles?

A polygon.

---- nope sorry.. i could have two lines they are non-collinear .. and they meet - ie. they intersect.. and well, they will have = made an angle - by definition of what it means .. when two non-collinear lines meet..

polygon has to be closed..

there is nothing in the statement of the problem that one can use to state even is there are more than 2 sides.. let alone if its a closed set..