Regular heptagon, finding value of unknowns

AI Thread Summary
To find the unknown angles in a regular heptagon, the interior angle is calculated as 128.57 degrees, derived from the formula (n-2)*180/n. The discussion suggests focusing on smaller components, such as the triangle formed at the top of the heptagon, to simplify the problem. Participants are encouraged to identify known angles within that triangle to aid in determining the unknowns. Understanding the relationship between the angles in the triangle and the interior angle of the heptagon is crucial for solving the problem. This approach can effectively lead to finding all unknown angles in the heptagon.
Frank212
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Homework Statement


bandicam 2016-08-14 13-44-31-309.jpg


Homework Equations


(n-2)*180[/B]

The Attempt at a Solution


11.a: 7-2=5, 5*180= 900. 900/7= 128.57 degrees
b. How do you find the unknowns?[/B]
 

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Frank212 said:
How do you find the unknowns
It may help to concentrate on one small piece. Look at the triangle at the top.
 
haruspex said:
It may help to concentrate on one small piece. Look at the triangle at the top.
How do I use 128.57 degrees to help me find the unknowns?
 
Frank212 said:
How do I use 128.57 degrees to help me find the unknowns?
Do you know any of the angles in the top triangle?
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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