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polygon

by shashank.ism » Tue Feb 09, 2010 1:04 pm
Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90deg or concave if the internal angle is 270deg. If the number of convex corners in such a polygon is 25, the number of concave corners must be

20
0
21
22
23
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by harsh.champ » Wed Feb 10, 2010 11:54 pm
shashank.ism wrote:Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90deg or concave if the internal angle is 270deg. If the number of convex corners in such a polygon is 25, the number of concave corners must be

20
0
21
22
23

In this kind of polygon, the number of convex angles will always be exactly 4 more than the number of concave angles (why?).
Note : The number of vertices should be even. Hence the number of concave and convex corners should add up to an even number. This is true only for the answer choice C.
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by sparky_paris » Thu Feb 11, 2010 4:45 pm
The answer is indeed 21. The number of concave angles is 4 less than convex.. why .. because to form a closed polygon you need this condition given that all sides are parallel to the x or y axes
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by jeffedwards » Thu Feb 11, 2010 6:30 pm
Draw a couple examples like this and count. The rule holds to be true. Drawing always helps me.
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by swapna » Thu Feb 11, 2010 7:48 pm
i have a doubt here...how can the side be parallel to x or y axes if its 270 degrees...can some clarify??
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by ajith » Thu Feb 11, 2010 11:51 pm
swapna wrote:i have a doubt here...how can the side be parallel to x or y axes if its 270 degrees...can some clarify??
Image

In the pic above DEF has internal angle 270 degree yet DE is parallel to Y axis and EF is parallel to X axis.
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by vscid » Sat Feb 13, 2010 1:56 pm
sparky_paris wrote:The answer is indeed 21. The number of concave angles is 4 less than convex.. why .. because to form a closed polygon you need this condition given that all sides are parallel to the x or y axes
Is this some kind of a rule or something?
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by okigbo » Sun Feb 14, 2010 8:03 am
What is the source to this problem?

I've never seen a problem like this on OG materials... has anyone?
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by harsh.champ » Thu Feb 18, 2010 5:13 am
vscid wrote:
sparky_paris wrote:The answer is indeed 21. The number of concave angles is 4 less than convex.. why .. because to form a closed polygon you need this condition given that all sides are parallel to the x or y axes
Is this some kind of a rule or something?
I also asked the same question in a preceding post.
My guess is this rule holds true if we start drawing different polygons and test this rule.

But in my formal education,I have never come across this rule.
Is it Ok to use it as a thumb rule?

Can anybody post the link to "All the pertaining geometry rules"??
It would be better for everyone to go through it .
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