The Maximum Enneagon

Geometry Level 2

What is the maximum number of interior right angles than can be used to form an irregular enneagon (9-sided polygon)?

8 6 5 7

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W Rose by W Rose , 63, USA

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1 solution

Eziz Hudaykulyyev
Jan 22, 2016

Regular 9gon's one sides angle is 140. Total interior angle will be 9x140=1260. Irregular 9gons angles can be maximum 359 degree. Lets assume maximum number of right angles is 8, thus remainig angle will equal to 1260-8x90=540. Obviosly it cant be. Lets take 7 right angles, sum of remaining angles will be 1260-7x90=660. And average value of remaining angle will be 330. Our answer is 7.

14 Helpful 0 Interesting 2 Brilliant 0 Confused

Excellent explanation of a fundamental geometric proof!

W Rose - 5 years, 4 months ago

Careful. 1260 − 7 × 90 = 630 1260 - 7\times90 = 630 , so the other two angles average 31 5 ∘ 315^\circ . It would also be sensible to show that 7 7 right angles are possible in an enneagon, as below (in this case, the other two angles are both exactly 31 5 ∘ 315^\circ :

Mark Hennings - 5 years, 3 months ago

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