Can pentagons that are known to tile the plane be ruler and compass construction?

Question

There are 15 types of convex pentagons are known to tile the plane monohedrally.

https://en.wikipedia.org/wiki/Pentagonal_tiling

I am wondering if all these 15 types pentagons are ruler and compass construction. If not, which of them can be (or not be) ruler and compass construction.

I have tried type 14 and 15 pentagons, both are ok.

Answer 1

A small observation, a simple class of tiling pentagons are the ones that have two parallel sides. Clearly not all such pentagons can be constructed with ruler and compass. But then we can construct a whole lot of them, just draw two parallel lines, and then have some random choices.