In a convex polygon, exactly five of the interior angles are obtuse. The largest possible number of sides for this polygon is
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Solution

Since exactly five interior angles are obtuse, then exactly five exterior angles are acute and the remaining angles must be obtuse. Since we want the maximum number of obtuse angles, assume that the five acute exterior angles have a sum less than 90r. Since obtuse angles are greater than 90 r, we can only have three of them.

Thus, the given polygon can have at most $3+5=8$ sides.

ANSWER: (B)

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