19.44 Extend the sides of a regular $n$-sided polygon to form a star, then the angle at the vertices of the star is 
(A) $\frac{360^{\circ}}{n}$.
(B) $\frac{(n-4) 180^{\circ}}{n}$.
(C) $\frac{(n-2) 180^{\circ}}{n}$.
(D) $180^{\circ}-\frac{90^{\circ}}{n}$.
(E) $\frac{180^{\circ}}{n}$.
(3rd American High School Mathematics Examination, 1952)
[Solution] For a regular $n$-sided polygon, the measure of each vertex angle is $\frac{(n-2) 180^{\circ}}{n}$. When forming a star, each star vertex and the original regular polygon vertex form an isosceles triangle.
Using the exterior angle property of a triangle, the angle at each star vertex can be calculated as
$$
180^{\circ}-2\left[180^{\circ}-\frac{(n-2) 180^{\circ}}{n}\right]=\frac{n-4}{n} \cdot 180^{\circ} \text {. }
$$

Therefore, the answer is $(B)$.