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Question
What is the greatest number of acute angles that can occur in a convex n gon
What is the greatest number of acute angles that can occur in a convex n gon
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Solution
The maximum number of acute interior angles in a convex n-gon is 3.
Exterior angles add up to 360 degrees.
Three obtuse exterior angles already have a sum exceeding 270 degrees, leaving less than 90 degrees for any remaining exterior angles if the polygon is going to be convex.
Thus, the maximum number of obtuse exterior angles is three, and so the maximum number of acute interior angles is three.
The maximum number of acute interior angles in a convex n-gon is 3.
Exterior angles add up to 360 degrees.
Three obtuse exterior angles already have a sum exceeding 270 degrees, leaving less than 90 degrees for any remaining exterior angles if the polygon is going to be convex.
Thus, the maximum number of obtuse exterior angles is three, and so the maximum number of acute interior angles is three.
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