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What is the greatest number of interior right angles a convex octagon can have?

 Nov 4, 2019
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A convex octagon has interior angles that add to (8 - 2)(180) = 1080 degrees

If there is one right angle, the remaining angles must average (1080-90) / 7 ≈ 141.4 degrees

If there are two right angles, the remaining angles must average (1080 - 180) / 6 = 150 degrees

If there are three right angles, the remaining angles must average (1080 - 270) / 5 = 162 degrees

If there are four right angles, the remaining angles must average (1080 - 360) / 4 = 180 degrees, but this isn't possible while remaining convex.

So the largest possible number of right angles is three.

 

(Thank you for helping me with the other math problems I posted earlier... laugh)

 Nov 4, 2019

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