It is a theorem of Gauss (and... Wantzel? Gauss did sufficient, someone else did necessary) that we can construct a regular $n$-gon via a straight edge and compass if and only if $n$ is of the form $p_1p_2\ldots p_i2^j$ where the $p_k$ are distinct Fermat Primes.
Now, if you can construct an angle of $d$-degrees then you can use this to construct a regular $n$-gon, where $n$ is such that $d.n=0 \text{ mod }360$ (draw your angle on a circle, follow where your lines hit the edge and repeat - basically, work out the order of $d$ in the cyclic group of order $360$).
If $d=110$ then $n=36=2^{2}3^{2}$.
If $d=85$ then $n=72=2^{3}3^{2}$.
Your Fermat Primes are $3$, $5$, $17$, $257$ and $65537$ (although I believe it is an open question if there are any more). However, they each must occur no more than once in the prime factorisation of $n$. $3$ appears twice in both $36$ and $72$ (aka $9$ divides them both), so we cannot construct a $36$-gon nor a $72$-gon. Thus, we cannot construct angles of either 110 or 85 degrees.