Geometrical Inequalities 2
Geometry
Level
2
Exactly five interior angles of a convex polygon are obtuse. Find the maximum possible number of sides for such a polygon.
The answer is 8.
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1 solution
As we know the the sum of internal angles of a convex polygon is : (n-2)*180
and we know that the maximum sum of three obtuse angles is 3*179
and we count that other angles of the polygon are (n-3)*X
X is a variant that should be less than 90 ( right angle )
(3 179)+((n-3) X) = (n-2)*180
by the description when n=8 , x is less than 90 and that's the right answer.