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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°.

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โˆ™ 2009-02-23 00:10:04
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Q: How do you divide a polygon into triangles to find the sum of its interior angles?
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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 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 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.


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.


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 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.


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.


How can you find the area of a polygon that is not one for which you know an area formula?

Divide the polygon into triangles. Calculate the areas of the triangles and then sum these.


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 type of polygon has the sum interior angles of 3420?

The sum of angles of a regular polygon: (n - 2)180 = 3,420 180n - 360 = 3,420 add 360 to both sides; 180n = 3,780 divide both sides by 180; n = 21 Thus a 21-side regular polygon has the sum of interior angles 3,420 degrees.


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°


How do you find the interior angle of a polygon?

The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. Once you have the sum, divide by the number of sides to find an individual angle.


How can you determine the number of degrees of the interior angles of a polygon?

A closed polygons internal angles always add up to 360 degrees. If all the angles are the same in the polygon then divide 360 by the number of angles. This would give you each intersects interior angle. This only works for regular polygons though like pentagons heptagons ect.


What are the interior angles of a 150 sided polygon?

To figure that out you simply divide 360o by 150: 360o / 150 = 2.4o or 2 2/5o


The sum of the interior angle measures of an octagon?

To find interior angle measurements, you must divide the shape into triangles by drawing diagonal lines. The diagonal lines draw triangles, and the interior angle measure of triangles are always 180 degrees. The sum of interior angles of an octagon is 1080 degrees. How ever many triangles you have, multiply it by 180. See octagons in the link for more help,


Formula of N-sided polygons?

Sum of interior angles of an n-sided polygon = (n-2) x 180Sum of one interior angle of an n-sided polygon = (n-2) x 180 then divide by n.


How do you find area of an irregular polygon?

For example, you can divide the polygon into triangles, and calculate the area of each triangle.


How many sides does a polygon have if the measure of each exterior angle of a regular polygon is 45 degrees?

8 Since the sum of the exterior angles of any polygon is always 360, you can divide 360 by 45 to find the number of exterior angles, which is 8. That means 8 interior angles and eight sides as well.


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


Can a regular polygon have an interior angle of 157?

An interior angle of 157 degrees implies an exterior angles of 23 degrees (= 180-157). The exterior angle MUST divide 360 degrees. 23 does not divide into 360 so the answer is NO.


How do you find the number of sides of a polygon knowing the measure of one of its interior angles?

If it's a regular polygon then deduct the known angle from 180 degrees and divide the answer into 360 which will give the amount of sides.


How do you find a number of sides of a polygon with the measure of its interior angle?

If its a regular polygon then 180-interior angle and divide the answer into 360 which will give the number of sides of the polygon.


What is the size of an interior angle on a regular 15-sided shape?

156 degrees Sum of interior angles of a polygon=180(n-2), where n is the number of sides. To find one interior angle's measure, divide by the total number of angles, which is also the total number of sides.


How do you calculate interior angles?

The formula to find the measure of an interior angle in a regular polygon is [(n-2)(180)]/n In other words, you take the number of sides in a regular polygon, such as a rhombus, and subtract two. Then multiply that by 180. Lastly, divide by the number of sides.