He has been asked for the total interior angle of a polygon with nine sides...anyone give us some pointers on how to do this.
2006-10-11 05:42:54 · 17 answers · asked by Anonymous in Education & Reference ➔ Homework Help
The formulae for total interior angle of a n-side polygon is
(n-2) x 180
Therefore, for a polygon with nines sides, it is
(9-2) x 180 = 7 x 180 = 1260.
2006-10-11 05:47:34 · answer #1 · answered by Turtle 2 · 0⤊ 0⤋
The trick is to tuen the shape into a number of triangles and use the fact that a triangle's interior angles add up to 180. So a square can be cut through the diagonal to make two trianles, and 2 x 180 = 360 (which is right of course, a square has 4 x 90 corners).
The formula for working out the total interior angles derived from this is
Sum of Interior Angles = 180(n-2) =, where n is the number of sides.
Hence, for a 9-sided polygon you have
180(9-2) = 180(7) = 1260 degrees
Hope this helps
2006-10-11 05:49:12 · answer #2 · answered by satyricon_uk 3 · 0⤊ 0⤋
The formula we use to find the sum of the interior angles of any polygon comes from the following idea:
Suppose you start with a pentagon. If you pick any vertex (the point where any 2 sides meet) of that figure, and connect it to all the other vertices, how many triangles can you form?
If you start with vertex A and connect it to all other vertices (it's already connected to B and E by sides) you form three triangles. Each triangle contains 1800. So the total number of degrees in the interior angles of a pentagon is:
3 1800 = 5400
Using the pentagon example, we can come up with a formula that works for all polygons. Notice that a pentagon has 5 sides, and that you can form 3 triangles by connecting the vertices. That's 2 less than the number of sides. It's the same principle for all polygons. If we represent the number of sides of a polygon as n, then the number of triangles you can form is (n-2). Since each triangle contains 1800, that gives us the formula:
2006-10-11 05:53:46 · answer #3 · answered by textkitten 3 · 0⤊ 0⤋
To find the sum of the interior angles of any regular polygon, use the formula:
(n-2) x 180 [where n = number of sides]
eg. a quadrilateral has 4 sides.
(4-2) x 180
=2 x 180
=360
Hope this helps!
2006-10-11 06:03:30 · answer #4 · answered by Bug 2 · 0⤊ 0⤋
The easiest way to work this out for any polygon follows. Take a ruler, and starting at one corner, divide the polygon into triangles from that one corner. Each triangle contains 180 degrees, so multiply the number of triangles by 180 degrees, to work out the total of the interior degrees. This is how we learned it when I was at school.
2006-10-11 06:43:17 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Don't all angles always add up to 360? No I'm wrong it's "The sum of the interior angles of a simple n-gon is (nâ2)Ï radians or (nâ2)180 degrees," so (9-2)180 = 1260
2006-10-11 05:57:54 · answer #6 · answered by sunshine 4 · 1⤊ 0⤋
3 angles = 180 degrees always
4 angles = 360 degrees always
...
2006-10-11 05:48:15 · answer #7 · answered by Puppy Zwolle 7 · 0⤊ 0⤋
if all the angles are the same times by 9. if the angles are diffrent add them up.
2006-10-11 05:53:20 · answer #8 · answered by monkey 1 · 0⤊ 0⤋
the answer should be 360 degrees
2006-10-11 05:52:06 · answer #9 · answered by Amy 1 · 1⤊ 0⤋
it will be (n-2)pi=7*180=1260*
2006-10-11 05:50:38 · answer #10 · answered by raj 7 · 0⤊ 0⤋