Let's construct a $12.75^{\circ}$ angle as simply as possible.
Among the divisions of a circle using a compass and ruler, in practice, only the division into 6 and 5 parts (construction of a regular hexagon or pentagon) are feasible. Essentially, this means we can directly construct angles of $60^{\circ}$ and $72^{\circ}$. By halving, adding, and subtracting, the $12.75^{\circ}$ angle can be constructed in many ways. However, from a practical standpoint, only constructions with the fewest steps and preferably larger angles should be considered.

For example:

$$
12.75^{\circ}=\frac{72^{\circ}+30^{\circ}}{2^{3}}, \quad \text { or } \quad 12.75^{\circ}=\frac{36^{\circ}+15^{\circ}}{2^{2}}
$$

Kiss Krisztina (Debrecen, Svetits g. II. o. t.)