## Polygon types

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
caters
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Joined: Sat Mar 15, 2014 11:14 pm
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### Polygon types

Equilateral pentagon: all sides are equal and all sets of 3 adjacent angles are in a range of angles(doesn't have to be regular meaning it is also equiangular)

Pentagons can have 1-4 acute angles, 1-3 right angles,1-5 obtuse angles, and 1-2 reflex angles.
They all have to add up to 540
with a 4th right angle the last angle would be 180 degrees which is always a problem with pentagons. Thus a pentagon cannot have a 4th right angle.
Is there a way to figure out all the different angles possible in a pentagon with these 2 sentences about angles? And is this a sum of permutations or a sum of combinations?

I am assuming all angle measurements are integers that when you take the sum add up to 540.

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Polygon types

Equilateral pentagon: all sides are equal and all sets of 3 adjacent angles are in a range of angles(doesn't have to be regular meaning it is also equiangular)

Pentagons can have 1-4 acute angles, 1-3 right angles,1-5 obtuse angles, and 1-2 reflex angles.
They all have to add up to 540
with a 4th right angle the last angle would be 180 degrees which is always a problem with pentagons. Thus a pentagon cannot have a 4th right angle.
Is there a way to figure out all the different angles possible in a pentagon with these 2 sentences about angles? And is this a sum of permutations or a sum of combinations?

I am assuming all angle measurements are integers that when you take the sum add up to 540.
Which "2 sentences"? What does the homework prob say EXACTLY?

caters
Posts: 7
Joined: Sat Mar 15, 2014 11:14 pm
Contact:

### Re: Polygon types

Equilateral pentagon: all sides are equal and all sets of 3 adjacent angles are in a range of angles(doesn't have to be regular meaning it is also equiangular)

Pentagons can have 1-4 acute angles, 1-3 right angles,1-5 obtuse angles, and 1-2 reflex angles.
They all have to add up to 540
with a 4th right angle the last angle would be 180 degrees which is always a problem with pentagons. Thus a pentagon cannot have a 4th right angle.
Is there a way to figure out all the different angles possible in a pentagon with these 2 sentences about angles? And is this a sum of permutations or a sum of combinations?

I am assuming all angle measurements are integers that when you take the sum add up to 540.
Which "2 sentences"? What does the homework prob say EXACTLY?

It says:
Pentagons can have 1-4 acute angles, 1-3 right angles, 1-5 obtuse angles, and 1-2 reflex angles.
The angles all have to add up to 540
With a 4th right angle you would have a quadrilateral
The angles are integers between 0 and 180 but not including 0 and 180

How many pentagons are there as far as angles?