How do you find the sum of the interior angles of a polygon with 8 sides?

Therefore, to find the sum of the interior angles of a polygon, we use the formula: Sum of interior angles = (n − 2) × 180° where 'n' = the number of sides of a polygon.

What is the total sum of the 8 angles?

Accordingly, the sum of the interior angles of a polygon having 8 sides = (8–2)180° = 1080° .

What is the sum of the interior angles of the polygon pictured below with 8 sides?

Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080° .

What is the angle sum formula?

The sum of the interior angles of a given polygon = (n − 2) × 180° , where n = the number of sides of the polygon.

What is the formula for interior angle sum property?

The angle between two sides of a triangle is called the interior angle. It is also known as the interior angle property of a triangle. This property states that the sum of all the interior angles of a triangle is 180°. If the triangle is ∆ABC, the angle sum property formula is ∠A+∠B+∠C = 180° .

What are the interior angles of a shape with 8 sides?

∴ The interior angle of a regular octagon = (8−2)×180∘8 = 6×180∘8 = 135∘

What are the angles of a polygon with 8 sides?

Sides of an Angle: The two straight lines that join to form an angle are the sides of the angle . Vertex: A vertex of an angle is the point at which the two lines or rays meet to form the angle.

What is the sum of the interior angle measures of a convex 8 sided polygon?

Subtract each angle from 180 degrees to get the internal angles, you see that the answer is 8 x 180 - 360 = 1080 degrees . Check this for a regular octagon, in which the internal angles are 135 degrees. You see that 8 x 135 = 1080, so it checks out.

What is the formula for the sum of the interior angles of a octagon?

Octagon is a polygon with 8 sides. For an n-sided polygon, the formula to calculate the sum of interior angles is given by (n - 2) × 180° . So, since the octagon has 8 sides, the sum of the interior angles will be (8 - 2) × 180° = 1080°.

How to find the sum of interior angles of a rectangle?

We also know that a rectangle (or any quadrilateral for that matter) has 4 sides: This means that the sum of all the internal angles of a rectangle is 180° × (4 - 2) = 180° × 2 = 360° . Hence, the sum of all the internal angles of a rectangle (or any quadrilateral) is 360°.

Do all interior angles add up to 360°?

Every shape has a unique sum of its interior (inside) angles : Triangle (3 sides): 180 degrees. Square (4 sides): 360 degrees. Pentagon (5 sides): 540 degrees.

How to calculate interior angle?

The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides .

What is the sum of the interior angles of a shape with 7 sides?

We know that sum of interior angles of an n-sided polygon is given by the formula: (n - 2) × 180 degrees. For a heptagon, the number of sides is seven; hence n = 7. (7 - 2) × 180 degrees = 900 degrees .

How to Calculate the Sum of Interior Angles: 8 Steps (2024)

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Co-authored byDavid Jia

Last Updated: October 3, 2022Fact Checked

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A polygon is any closed figure with sides made from straight lines. At each vertex of a polygon, there is both an interior and exterior angle, corresponding to the angles on the inside and outside of the closed figure. Understanding the relationships that govern these angles is useful in various geometrical problems. In particular, it is helpful to know how to calculate the sum of interior angles in a polygon. This can be done using a simple formula, or by dividing the polygon into triangles.

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Using the Formula

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1
Set up the formula for finding the sum of the interior angles. The formula is , where is the sum of the interior angles of the polygon, and equals the number of sides in the polygon.^[1]^[2]
- The value 180 comes from how many degrees are in a triangle. The other part of the formula, is a way to determine how many triangles the polygon can be divided into. So, essentially the formula is calculating the degrees inside the triangles that make up the polygon.^[3]
- This method will work whether you are working with a regular or irregular polygon. Regular and irregular polygons with the same number of sides will always have the same sum of interior angles, the difference only being that in a regular polygon, all interior angles have the same measurement.^[4] In an irregular polygon, some of the angles will be smaller, some of the angles will be larger, but they will still add up to the same number of degrees that are in the regular shape.
2
Count the number of sides in your polygon. Remember that a polygon must have at least three straight sides.^[5]
- For example, if you want to know the sum of the interior angles of a hexagon, you would count 6 sides.
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3
Plug the value of into the formula. Remember, is the number of sides in your polygon.^[6]
- For example, if you are working with a hexagon, , since a hexagon has 6 sides. So, your formula should look like this:
4
Solve for . To do this, subtract 2 from the number of sides, and multiply the difference by 180. This will give you, in degrees, the sum of the interior angles in your polygon.^[7]
- For example, to find out the sum of the interior angles of a hexagon, you would calculate:
  
  So, the sum of the interior angles of a hexagon is 720 degrees.

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Drawing Triangles

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1
Draw the polygon whose angles you need to sum. The polygon can have any number of sides and can be regular or irregular.
- For example, you might want to find the sum of the interior angles of a hexagon, so you would draw a six-sided shape.
2
Choose one vertex. Label this vertex A.
- A vertex is a point where two sides of a polygon meet.
3
Draw a straight line from Point A to each other vertex in the polygon. The lines should not cross. You should create a number of triangles.
- You do not have to draw lines to the adjacent vertices, since they are already connected by a side.
- For example, for a hexagon you should draw three lines, dividing the shape into 4 triangles.
4
Multiply the number of triangles you created by 180. Since there are 180 degrees in a triangle, by multiplying the number of triangles in your polygon by 180, you can find the sum of the interior angles of your polygon.^[8]
- For example, since you divided your hexagon into 4 triangles, you would calculate to find a total of 720 degrees in the interior of your polygon.

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How do I find a single interior angle?
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Work out what all the interior adds up to, then divide by however many sides the shape has.
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How do I calculate the number of sides of a polygon if the sum of the interior angles is 1080?
Donagan
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Divide that sum by 180°, then add 2. In this example, 1080° / 180° = 6. 6 + 2 = 8. The polygon has 8 sides.
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Question
If two equilateral triangles are placed together to form a rhombus, how do I calculate the value of each interior angle of this rhombus, and how do I find the sum?
Donagan
Top Answerer
In the rhombus you describe, the two smaller interior angles would each be 60°, and the two larger interior angles would each be 120°. You wouldn't have to calculate the angles. Simple inspection of the rhombus and the two triangles would show what the angles are, given that equilateral triangles have three 60° angles. The sum is 60° + 60° + 120° + 120°.
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Angle Properties of Triangles - Wyzant Lessons

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Check your work on a piece of paper using a protractor to sum the interior angles manually. When doing this, be careful while drawing the polygon's sides as they should be linear.
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References

↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021
↑ http://www.mathsisfun.com/geometry/interior-angles-polygons.html
↑ https://www.bbc.co.uk/bitesize/guides/zshb97h/revision/6
↑ https://www.bbc.co.uk/bitesize/guides/zshb97h/revision/6
↑ https://www.bbc.co.uk/bitesize/guides/zshb97h/revision/6
↑ https://www.mathsisfun.com/geometry/interior-angles-polygons.html
↑ https://www.mathsisfun.com/geometry/interior-angles-polygons.html
↑ https://www.cuemath.com/geometry/sum-of-angles-in-a-polygon/

About This Article

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David Jia

Academic Tutor

This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 423,591 times.

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Co-authors: 17

Updated: October 3, 2022

Categories: Geometry

Article SummaryX

To calculate the sum of interior angles, start by counting the number of sides in your polygon. Next, plug this number into the formula for the "n" value. Then, solve for "n" by subtracting 2 from the number of sides and multiplying the difference by 180. This will give you, in degrees, the sum of the interior angles in your polygon! To learn how to calculate the sum of interior angles by drawing triangles, read on!

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How to Calculate the Sum of Interior Angles: 8 Steps (2024)

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