Problem:
Exactly three of the interior angles of a convex polygon are obtuse. What is the maximum number of sides of such a polygon?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For any convex -gon, the sum of the interior angles is (. If an -gon has exactly obtuse interior angles, then the remaining angles have measure at most each and the obtuse angles have measure less than together. Thus
To show is possible, "distort" an equilateral triangle as shown.
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