An archaeological discovery of a regular polygon fragment, as shown in the figure: Using only a set of student triangular rulers and a pencil as tools, please determine the number of sides of this regular polygon.
(Explanation: The given regular polygon fragment has $\angle \mathrm{EAB}=\angle \mathrm{ZFBA}=\angle 165^{\circ}$, and contestants need to measure it manually.)
27. Answer: 24

Analysis: Using a set of student triangular rulers and a pencil, the angle $\angle E A B=90^{\circ}+45^{\circ}+30^{\circ}=165^{\circ}$ can be measured.
From $(\mathrm{n}-2) \times 180^{\circ}=\mathrm{n} \times 165^{\circ}$, we get $\mathrm{n}=24$.
Or as shown in the figure, extend $\mathrm{EA}$ to $\mathrm{C}$, use an isosceles right triangular ruler to draw $\angle \mathrm{BAD}=45^{\circ}$, and then use the smaller acute angle of another triangular ruler to measure $\angle \mathrm{CAD}=30^{\circ}$, thus $\angle \mathrm{BAC}=45^{\circ}-30^{\circ}=15^{\circ}$.

From $\mathrm{n} \times 15^{\circ}=360^{\circ}$, we solve to get $\mathrm{n}=24$.