0
How do you divide a polygon into triangles to find the sum of its interior angles?
Wiki User
∙ 15y ago
If a regular polygon has n sides, then the number of triangles in that polygon is n - 2. thus, the sum of its interior angles is equal to (n - 2)180°.
Wiki User
∙ 15y ago
Add your answer:
Earn +20 pts
What is the sum of the interior angles of a twenty sided polygon?
Use the formula below to calculate the sum of the interior angles of any polygon with n-number of sides: n * (180o) - 360o or (n-2) * 180o And to find the measurement of each interior angle divide this number by the number of sides of the polygon. So for a 20-sided polygon, the sum of the interior angles would be: 20*180o - 3600 = 3240o or (20-2) * 180o = 3240o And each interior angle would measure 3240o/20 or 162o == ==
What are the interior angles of a 54 sided polygon?
To figure that out you must divide: 360 degrees / 54 = 6.67 degrees or 6 2/3 degrees
What is the measure of each angle of a regular polygon with 7 sides?
A regular polygon has sides of equal length, as well as interior angles of equal measure. But for any regular polygon, the sum of the measures of the exterior angles is 360 degrees. You can use this information to find out the measure of an interior angle, because the sum of the measures of each interior/exterior pair of angles is always 180 degrees. So to find the answer to this problem, divide 360 by 7. Each exterior angle is about 51.4 degrees. Subtract that number from 180. Each interior angle is about 128.6 degrees.
Find the size of each interior angle of 6 sided regular polygon?
To answer this question, you need to know a few things, which you probably know already:Any two angles formed by a straight line and a line coming off it in any direction will add to 180 degrees.There are 360 degrees in a circle.In a regular polygon, all of the interior angles will be equal. (I'm sure there's no need to tell you what an interior angle is)Now, if you think about it, in order for the hexagon (in other words, your 6-sided regular polygon; I'm going to call it a hexagon because it's shorter) be complete, the line that forms the outside of it has to go all the way around in a sort of circle. If you imagine that each side of the hexagon extends out in one direction, like a pinwheel, then the total of those small outside angles is 360 degrees.There are 6 of those angles, so 360 divided by 6 gives 60 degrees per Exterior Angle in a hexagon.Now, notice that there is one of these Exterior Angles per Interior Angle, and that the two add to 180 degrees (for the reasons stated above).So, 180 minus 60 gives 120 degrees per interior angle!This method works for all regular polygons. There is another method as well: The total of the interior angles in a triangle is 180 degrees. Pick one vertex (corner) of the polygon and draw lines from it to all the other vertices. Count the number of triangles you see, and multiply that number by 180. This gives you the sum of the interior angles in that polygon. Then, if it's regular, divide by the number of interior angles to give you the value of each interior angle.Remember that both of these methods only work when the polygon is regular.WikipediaWictionaryChambers (UK)Google imagesGoogle defineThe Free DictionaryJoin exampleWordNetGoogleUrban DictionaryAnswers.comrhymezone.comMerriam-Webster0wvcidfjoguarm
Approximately how many degrees are in the measure of an interior angle of a regular heptagon?
The measure of the interior angles of a regular heptagon is approximately 128.6 degrees. There are 2 ways to work this out: Find the total of all the angles and divide by 7: In an n-sided figure the interior angles sum to (n-2) x 180 degrees. For a heptagon, n=7, so total angles = (7-2) x 180 = 5 x 180 = 900 degrees So each angle = 900 / 7 ~= 128.6 degrees. Calculate the exterior angle and then subtract from 180 degrees to get the interior angle: The sum of the exterior angles of a polygon is 360 degrees; Divide 360 degrees by the number of angles (= number of sides) Exterior angle of heptagon is 360 / 7 ~= 51.4 degrees; Interior angle ~= 180 - 51.4 = 128.6 degrees
What is the sum of the interior angle of a 13-sided polygon?
The sum of the interior angles of a triangle is 180 deg. For a convex polygon with n sides we can divide it to n-2 triangles. So the answer, if the polygon is convex, is (13-2)*180= 1980 deg * * * * * The polygon need not be convex. The formula for the sum of the interior angles is valid as long as the polygon is simple - that it, its sides do not cross each other inside the polygon.
How do angles of heptagon add up too 900?
If you select one vertex of a heptagon and draw diagonals to all other vertices, you will divide the heptagon into 5 triangles such that the interior angles of the heptagon add up to the same sum as the interior angles of the five triangles.Now the sum of the interior angles of one triangle is 180 degrees. So for 5 triangles you get 5*180 = 900 degrees.In general, the interior angles of a polygon with n vertices is (n - 2)*180 degrees.
What is the sum of interior angles of a 17 sided polygon?
The sum of the interior angles of a 17 sided polygon add up to 2700 degrees.
How do I get the degrees in the interior angles of a polygon?
The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. To find an individual angle, divide that number by n.
How to find interior angle of a regular polygon?
You use the fact that the sum of the interior angles of a regular polygon with n sides is:180(n-2) degreesNow you have the sum of measures of all the interior angles so divide that by n and you have the measure of each interior angle.
If the interior angle of a regular polygon is 156 degrees how many sides does it have?
The interior angle is the angle formed from two sides of a nth-sided polygon. Because the polygon is regular, all angles formed from any two sides of the polygon are equal. It can be proven, but I won't attempt to, that to find the amount of sides, you use 180-[interior angle], and divide the answer by 360. In this case, 180-156=24, 360/24= 15, thus the polygon has 15 sides. One way to prove it is to imagine the polygon and divide it into isosceles triangles. But I won't go there.
What is the sum of the measures of the interior angles of a 14- sided polygon?
The 14 interior angles add up to 2160 degrees
What is the measure of each interior angle in a convex polygon?
The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. Divide that by the number of sides.
How do you find the number of sides in an equiangular polygon given the measures of the interior angles?
Type your answer here... The sum of the angles in all polygons is 360 degrees. Thus, if you know the measure of the interior angles you can divide 360 by the measurement to find out how many interior angles and sides there are.
How do you get the square inches of a polygon?
In general, you divide up the polygon into triangles, calculate the areas of the triangles and then sum these.
What is the measure of an interior angle and an exterior angle of a nonagon?
The sum of the interior angles of a polygon is 2n-4 Right Angles For a nonagon (2x9)-4 RAs = 14x90°=1260° To find the interior angle of a regular nonagon, divide this by 9 which gives 140° To find the exterior angle, subtract this from 180 and you get 40°. The sum of the exterior angles of a polygon is 360°, so for a regular polygon you can also divide this by the number of sides, which in this case also gives: 360° ÷ 9 = 40°
What is the sum of the interior angles of a twenty sided polygon?
Use the formula below to calculate the sum of the interior angles of any polygon with n-number of sides: n * (180o) - 360o or (n-2) * 180o And to find the measurement of each interior angle divide this number by the number of sides of the polygon. So for a 20-sided polygon, the sum of the interior angles would be: 20*180o - 3600 = 3240o or (20-2) * 180o = 3240o And each interior angle would measure 3240o/20 or 162o == ==
