17) Consider a five-pointed star inscribed in a circle. What is the sum of the angles with vertices at the points of the star?
(A) $100^{\circ}$
(B) $150^{\circ}$
(C) $180^{\circ}$
(D) $200^{\circ}$

(E) the data provided is insufficient.

![](https://cdn.mathpix.com/cropped/2024_04_17_d5d8199ad7e56b403760g-2.jpg?height=217&width=239&top_left_y=1331&top_left_x=1160)
17) The answer is (C). Each of the five angles of the star is an angle at the circumference, and each is subtended by an arc. The union of these arcs covers the entire circumference, and the sum of the lengths of these arcs is precisely the length of the entire circumference. It is known that angles at the circumference subtended by an arc are half the corresponding central angles. The sum of the angles with vertices at the points of the star is half the central angle subtended by the entire circumference, which is a full angle, hence the sum is $\frac{360^{\circ}}{2}=180^{\circ}$.