Difference between revisions of "1950 AHSME Problems/Problem 12"
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==Solution== | ==Solution== | ||
| − | + | By the Exterior Angles Theorem, the exterior angles of all convex polygons add up to <math>360^\circ,</math> so the sum <math>\boxed{\mathrm{(C)}\text{ remains constant}.}</math> | |
==See Also== | ==See Also== | ||
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[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:40, 27 February 2016
Problem
As the number of sides of a polygon increases from 
to 
, the sum of the exterior angles formed by extending each side in succession:
Solution
By the Exterior Angles Theorem, the exterior angles of all convex polygons add up to 
so the sum 
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
