PLEASE HELP
- Thread starter ticka06
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Ticka:
I think you better check this
http://www.math.com/school/subject3/les ... 2L1DP.html
I think that the sum of interior angles of a poligon will be the same for every poligon
I think you better check this
http://www.math.com/school/subject3/les ... 2L1DP.html
I think that the sum of interior angles of a poligon will be the same for every poligon
ticka06 said:I need to know What is the sum of the interior and of the exterior angles of a 100-gon?
Hi ticka06,
Memorize these two statements:
(1) The sum of the interior angles of a convex polygon is given by the formula 180(n-2) where n = the number of sides.
Example: Your 100-gon: Interior angle sum = 180(100-2) ==> 180(98) ==> 17640 degrees
(2) The sum of the exterior angles of a convex polygon is always 360 degrees.
Example: Your 100-gon: Exterior angle sum = 360 degrees.
Or,
if you are visual....
A regular n-gon consists of n isosceles triangles, all touching at the centre.
This gives n(180) degrees. Subtract the 360 degrees that all the central angles sum to for the interior angles at the perimeter.
If you draw a sketch, you can prove to yourself that the exterior angles equal the angles at the centre plus n(180) degrees.
The sum of the exterior angles is most certainly not 360 degrees.
It is 360 degrees if you extend the sides out and then measure those angles!
Remember, the actual exterior angles are all greater than 180 degrees.
Acute angles can be formed by extending each side outwards.
if you are visual....
A regular n-gon consists of n isosceles triangles, all touching at the centre.
This gives n(180) degrees. Subtract the 360 degrees that all the central angles sum to for the interior angles at the perimeter.
If you draw a sketch, you can prove to yourself that the exterior angles equal the angles at the centre plus n(180) degrees.
The sum of the exterior angles is most certainly not 360 degrees.
It is 360 degrees if you extend the sides out and then measure those angles!
Remember, the actual exterior angles are all greater than 180 degrees.
Acute angles can be formed by extending each side outwards.
chrisr said:The sum of the exterior angles is most certainly not 360 degrees.
What are you calling exterior angles? In most geometry textbooks they say flatly that the exterior angles of a polygon add to 360° This is only true if:
(a) You take only one per vertex, and
(b) Take all the angles that point in the same direction around the polygon.
chrisr said:It is 360 degrees if you extend the sides out and then measure those angles!
I assumed that to be the case
chrisr said:Remember, the actual exterior angles are all greater than 180 degrees.
Acute angles can be formed by extending each side outwards.
So if you are asked "What is the sum of the exterior angles of a polygon?" without any conditions, you will have to guess which one they mean. Usually they mean taking one per vertex, and the answer is 360°, although strictly speaking this is wrong.