# how to find the number of sides of a regular polygon when given the interior angle

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Guys, does anyone know the answer?

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## How to find the number of sides of a polygon when given the interior angle sum? [Solved]

To find the number of sides of a polygon when given the sum of interior angle, we use the formula: Sum of interior angles = (n - 2) × 180, where n is the number of sides.

## How to find the number of sides of a polygon when given the interior angle sum?

Polygons are closed curves made of line segments. The polygons with equal sides and angles are called regular polygons. Each polygon has a fixed sum of interior angles depending on its number of sides.

## Answer: To find the number of sides of a polygon when given the sum of interior angles, we use the formula: Sum of interior angles = (n - 2) × 180, where n is the number of sides.

Let's understand this, with the help of an example.

**Explanation:**

We use the formula: Sum of interior angles = (n - 2) × 180, where n is the number of sides of the polygon, to solve the problem.

Now, let's assume we have an interior angle sum of 1620. We have to find the number of sides the polygon has.

Hence, using the above equation, (n - 2) × 180 = 1620.

Now, n - 2 = 1620 / 180.

Therefore, n - 2 = 9.

Finally, n = 11.

Hence, it is an 11-sided polygon.

### Hence, To find the number of sides of a polygon when given the sum of interior angles, we use the formula: Sum of interior angles = (n - 2) × 180, where n is the number of sides.

## How to Find the Number of Sides of a Polygon

Home ⋅ Math ⋅ Geometry ⋅ Solids

## How to Find the Number of Sides of a Polygon

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RELATED

### What Are the Characteristics of a Pentagon, Hexagon & Octagon?

By Chance E. Gartneer

A polygon by definition is any geometric shape that is enclosed by a number of straight sides, and a polygon is considered regular if each side is equal in length. Polygons are classified by their number of sides. For example, a six-sided polygon is a hexagon, and a three-sided one is a triangle. The number of sides of a regular polygon can be calculated by using the interior and exterior angles, which are, respectively, the inside and outside angles created by the connecting sides of the polygon.

Subtract the interior angle from 180. For example, if the interior angle was 165, subtracting it from 180 would yield 15.

Divide 360 by the difference of the angle and 180 degrees. For the example, 360 divided by 15 equals 24, which is the number of sides of the polygon.

Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon. For example, if the measurement of the exterior angle is 60 degrees, then dividing 360 by 60 yields 6. Six is the number of sides that the polygon has.

### Tips

Subtracting the interior angle from 180 gives the exterior angle, and subtracting the exterior angle from 180 gives the interior angle because these angles are adjacent.

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References

Wolfram Mathworld: Regular Polygon

Math Warehouse: Polygons, Formulas for Exterior Angles and Exterior Angles

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.

Photo Credits

Liquidlibrary/liquidlibrary/Getty Images

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## What Are the Characteristics of a Pentagon, Hexagon & Octagon?

•••

Updated April 25, 2017

By Richard Morgan

Polygons are mathematical concepts dealing with straight-line geometric figures. Polygons include shapes such as pentagons, hexagons, and octagons. Polygons can be considered convex, concave, or regular. Polygons can share more than one characteristic. For example, a regular pentagon is also considered convex.

## Pentagon

•••

Pentagons are geometric objects with five straight sides. The prefix “penta” comes from the Greek word for “five.” A regular pentagon has five equal sides. To find the area of a regular pentagon, divide the pentagon into five equal triangles. Calculate the area for one triangle and multiply that number by 5. The final answer is the area of the regular pentagon. For example, if the triangle area comes out to 2.1 square inches, multiply that by 5 — the area for the pentagon is 10.5 square inches.

## Hexagon

•••

Just as “penta” means “five,” “hexa” comes from the Greek word for “six.” A hexagon is a six-sided polygon. Just as a regular pentagon has five equal sides, a regular hexagon has six equal sides. The area of a hexagon can be found by creating six equal triangles from within the geometric shape. Find the area for one triangle and multiply the number by 6 to calculate the area of the hexagon. If the triangle area is 2.1 square inches, multiply that number by 6 — the area for the entire hexagon is 12.6 square inches.

## Octagon

## If the interior angle of a polygon is given, how do you find the number of its side?

Answer (1 of 7): Only if the figure is a regular polygon can we get the number of sides. Subtract the interior angle from 180 to get the exterior angle. Divide 360 by the exterior angle and you get the number of sides of the regular polygon. Example: The interior angle = 140 deg. So, the exter...

If the interior angle of a polygon is given, how do you find the number of its side?

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Sort Aldis Daniel

Studied at Maharishi Vidya Mandir, ChennaiAuthor has 299 answers and 327K answer views4y

Please do feel free to request me any of your doubts from maths and science. Just take a pic of the question and request me. I will answer asap. I will not look into comments, please request any doubts as questions.

Please upvote if you find it useful.

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What is the formula to find the number of sides of a regular polygon?

HsBadarinath

Ph.D. in Civil Engineering. Maths keeps one mentally active.Author has 60.9K answers and 37.4M answer views4y

Only if the figure is a regular polygon can we get the number of sides.

Subtract the interior angle from 180 to get the exterior angle. Divide 360 by the exterior angle and you get the number of sides of the regular polygon.

Example: The interior angle = 140 deg.

So, the exterior angle = 180–140 = 40 deg

No. of sides = 360/40 = 9.

Shree Ram Bhakt

ISC from Senior Secondary School Pawapuri NalandaAuthor has 112 answers and 355.3K answer views4y

If the interior angle of a regular polygon is given or sum of interior angles of any polygon is given, then we can easily find the number of its sides by the following relations,

If numbers of sides of polygon is n , then

Sum of interior angles = (2n - 4) × 90 degree

If the polygon is regular , then each interior angle of polygon = (2n - 4)/n × 90 degree.

These formulas can be easily proved .

Proof -

We know that sum of interior angles of a triangle is 180 degree.

If n is the number of sides of polygon, then polygon can be devided into n triangles which is clear from the above figure.

So, sum of all t

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Pradeep Hebbar

23+ years of Structural Engineering & Math enthusiasmAuthor has 5K answers and 2.5M answer views3y

Related

If an exterior angle of a regular polygon is equal to its interior angle, find the number of sides of the polygon?

In a regular n sided polygon,

Single interior angle = (2n-4) x 90/n

Single exterior angle = 360/n

Given: Exterior angle of a regular polygon is equal to its interior angle

(2n-4) x 90/n = 360/n

(2n-4) x 90 = 360 (2n-4) = 360/90 (2n-4) = 4 n=4,

Therefore, it is a regular polygon of 4 sides.

Ans: The polygon is a square.

Upvote if you agree!

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One of the interior angles of a regular polygon is 172 and the rest are equal to 158. How would one find the number of sides of the polygon?

What is the interior angle of a polygon with 20 sides?

Ved Prakash Sharma

Former Lecturer at Sbm Inter College, Rishikesh (1971–2007)Author has 12.1K answers and 12.1M answer views3y

Interior angle (x°) of a polygon = {(n-2)/n}.180°. [where n= number of sides.]

or. 180n-360= x.n or. 180.n-x.n=360 or. n.(180-x)=360

or. n = 360/(180-x). Answer.

Raj Sanjel

Lives in NepalAuthor has 122 answers and 339K answer views2y

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If a regular polygon has an interior angle of 175 degrees, how many sides does it have?

Polygon has 72 sides.

As we know each intetior angle of polygon = n(n-2)×180/n

So.A/Q n(n-2)×180/n=175

n=72Polygon has 72 sides.

As we know each intetior angle of polygon = n(n-2)×180/n

So.A/Q n(n-2)×180/n=175

n=72 Robinson Law

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Why didn't Mao's China invade Hong Kong and Macau?

Originally Answered: Why didn't Mao's China invade Hong Kong and Macao?

I can easily find many answers to this question:

1. HK & Macao are land connected to the mainland, both Mao and the British knew that HK was defenseless in face of Mao's huge army. The British never tried from the beginning to defend the leased territory at all. As for Macao, the Portuguese never disagreed that Macao has to be returned to the Chinese after the leased was over;

2. China, or PRC as it is called, needs HK's economy and its economic linkage to the world at large;

3. The lease for HK's New Territory would end in 1997 and the British needed to renegotiate for the future of HK man

Guys, does anyone know the answer?