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As figure above shows, there are eight central angles in a

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As figure above shows, there are eight central angles in a  [#permalink]

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01 Aug 2008, 09:28
As figure above shows, there are eight central angles in a circle, respectively are 10, 20, 30, ...80. An octagon yields when link the 8 intersections on the circumference. What is the measurement degree of the largest interior angle of the octagon?
A. 140
B. 145
C. 150
D. 160
E. 165

diagram is attached

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octagon.doc [42 KiB]

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Updated on: 01 Aug 2008, 09:37
165

Each angle creates an isoceles traingle, so there are 8 isoceles triangles in the diagram.

If the outer angles of the isoceles traingles are represented (such as the 10 dgree angle) by $$\frac{180 - 10}{2} = 90 - 5 = 85$$ and then the 20 degree angle one would be $$\frac{180-20}{2} = 90 - 10 = 80$$. In order to find the interior angle made up between the 10 degree portion and 20 degree portion, we need to add the adjacent angles. 80 + 85 = 165.

No other angles will be as large because the angle closer to the center of the circle will take up more of the 180 degrees of the isoceles triangle formed. For instance, the 80 degree portion. The other 2 angles are $$\frac{180-80}{2} = 90 - 40 = 50$$. This is certainly going to be a smaller angle than the interior angle between the 10 degree section and 20 degree section.
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Originally posted by jallenmorris on 01 Aug 2008, 09:32.
Last edited by jallenmorris on 01 Aug 2008, 09:37, edited 3 times in total.
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01 Aug 2008, 10:54
i dont get this question at all? can someone please explain what is being asked?
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01 Aug 2008, 11:00
fresinha12 wrote:
i dont get this question at all? can someone please explain what is being asked?

If you join all the points on the circumfrence of the circle you will get a octagon right? And it is askign for the largest interior angle in that octagon.

Logic here is that since all the ponts are on the circumfrence, the two sides of each triangle represents radius.. hence its an isoceles triangle.

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Re: OCTAGON &nbs [#permalink] 01 Aug 2008, 11:00
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As figure above shows, there are eight central angles in a

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