Are irregular polygons constructible?

Question

I don't know if my question doesn't make sense or it's just too elementary but I can't seem to find something anywhere in internet that guides me to a precise answer, I mean, in my head it's completely possible but the lack of answers made me question if I'm overlooking something. Anyways, is it possible to construct an irregular polygon?

Answer 1

Sometimes they can be and sometimes they can't.

For example, as you probably know, it is possible to construct a square and it is possible to construct an equilateral triangle. It is not too difficult, then, to construct the following 'house':

However, it is impossible to contruct this polygon, built from a regular heptagon:

Why is it impossible? Well, if we could construct that figure, then we could bisect the angle called $2a$ and construct the dotted line. Then we would have constructed a regular heptagon. But this is known to be impossible, since $7$ is prime and not of the form $2^{2^N}+1$.

Answer 2

The question doesn't really make sense as long as you don't specify which irregular polygon.

The vast majority of polygons aren't constructible. For examples, consider the polygon with an angle equal to an angle of a non-constructible regular polygon, or polygons with sides in a transcendental ratio.