1950 AHSME Problems/Problem 12

Problem

As the number of sides of a polygon increases from $3$ to $n$ , the sum of the exterior angles formed by extending each side in succession:

$\textbf{(A)}\ \text{Increases}\qquad\textbf{(B)}\ \text{Decreases}\qquad\textbf{(C)}\ \text{Remains constant}\qquad\textbf{(D)}\ \text{Cannot be predicted}\qquad\\ \textbf{(E)}\ \text{Becomes }(n-3)\text{ straight angles}$

Solution

By the Exterior Angles Theorem, the exterior angles of all convex polygons add up to $360^\circ,$ so the sum $\boxed{\mathrm{(C)}\text{ remains constant}.}$

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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1950 AHSME Problems/Problem 12

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