triangles from pentagons

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May 2010
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Hi. XD

1. a regular pentagon is divided into three triangles. calculate all the angles in each of the triangles.[/B] (a picture of the pentagon described above is attached). please explain too.

(the following info is relevant for the next 2 questions. btw the info the image of the pentagon is still relevant.)
the middle triangle in the pentagon has all acute angles and the left triangle has an obtuse angle. we will can a triangel type A if it is similar to the middle triangle MJL. we will call a triangle type B if it is similar to the left triangle MNJ.

2. show that a type A triangle can be divided into two triangles so that one is type A and the other is a type B

3. show that a regular pentagon can be divided into 2010 triangles so that one is a type A and 2009 of them are type B

Merci!
Joyousness
 

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Chris L T521

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Hi. XD

1. a regular pentagon is divided into three triangles. calculate all the angles in each of the triangles.[/B] (a picture of the pentagon described above is attached). please explain too.

(the following info is relevant for the next 2 questions. btw the info the image of the pentagon is still relevant.)
the middle triangle in the pentagon has all acute angles and the left triangle has an obtuse angle. we will can a triangel type A if it is similar to the middle triangle MJL. we will call a triangle type B if it is similar to the left triangle MNJ.

2. show that a type A triangle can be divided into two triangles so that one is type A and the other is a type B

3. show that a regular pentagon can be divided into 2010 triangles so that one is a type A and 2009 of them are type B

Merci!
Joyousness
The fact that (the years) "2010" and "2009" appear in the problem hint to us that this question may be from a maths competition.

This thread will remain closed as we conduct further investigation (we have zero tolerance for cheaters!!). If everything ends up being OK, it will be reopened.
 
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