Solution:
According to the given question,
\[AC\] is the side of a regular octagon,
\[\angle AOC\text{ }=\text{ }{{360}^{o}}/\text{ }8\text{ }=\text{ }{{45}^{o}}\]
Hence, \[arc\text{ }AC\]subtends \[\angle AOC\]at the centre and \[\angle ABC\]at the remaining part of the circle.
\[\angle ABC\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\angle AOC\]
So,
\[\angle ABC\text{ }=\text{ }{{45}^{o}}/\text{ }2\text{ }=\text{ }{{22.5}^{o}}\]