Study guides

☆☆

Q: How do you divide a polygon into triangles to find the sum of its interior angles?

Write your answer...

Submit

Still have questions?

Related questions

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.

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.

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.

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.

In general, you divide up the polygon into triangles, calculate the areas of the triangles and then sum these.

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.

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.

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.

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

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 == ==

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.

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°

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.

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.

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

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,

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.

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

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.

To figure that out you must divide: 360 degrees / 54 = 6.67 degrees or 6 2/3 degrees

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.

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.

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.

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.

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.