A rule of polygons is that the sum of the exterior angles always equals 360 degrees, but lets prove this for a regular octagon (8-sides).

You are watching: What is the measure of an exterior angle of a regular octagon?

First we must figure out what each of the interior angles equal. To do this we use the formula:

((n-2)*180)/n where n is the number of sides of the polygon. In our case n=8 for an octagon, so we get:

((8-2)*180)/8 => (6*180)/8 => 1080/8 = 135 degrees. This means that each interior angle of the regular octagon is equal to 135 degrees. 

Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon, so in this case each exterior angle is equal to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up to 180 degrees. 

And since there are 8 exterior angles, we multiply 45 degrees * 8 and we get 360 degrees.

This technique works for every polygon, as long as you are asked to take one exterior angle per vertex.


Upvote • 3 Downvote
Comments • 5
More
Report

Smith J.


Either I don"t understand your reasoning or you are talking bollocks. The INTERIOR angles add up tp 1080 in a polygon, ie 135 each.
Report

Jaycee D.


All you have to do is divide 360/n, n being the number of sides in the polygon
Reharbor

Jeanetto L.


I agree with the first person. it IS 135!!!
Report

Emily M.


Its wrong the answer is 45, all you have to do it take 360 and divide it by the number of sides (360/n) so lets say that the number of sides is 6, your equation would be 360/6 which would be and the answer would be 60. Check my math if you don"t think I"m right.
Report

JAde W.


This helped me so much thank you 
Report

Still looking for help? Get the right answer, fast.


Ask a question for free

Get a free answer to a quick problem. Most questions answered within 4 hours.


OR
Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.


¢ € £ ¥ ‰ µ · • § ¶ ß ‹ › « » > ≤ ≥ – — ¯ ‾ ¤ ¦ ¨ ¡ ¿ ˆ ˜ ° − ± ÷ ⁄ × ƒ ∫ ∑ ∞ √ ∼ ≅ ≈ ≠ ≡ ∈ ∉ ∋ ∏ ∧ ∨ ¬ ∩ ∪ ∂ ∀ ∃ ∅ ∇ ∗ ∝ ∠ ´ ¸ ª º † ‡ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Ø Œ Š Ù Ú Û Ü Ý Ÿ Þ à á â ã ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ø œ š ù ú û ü ý þ ÿ Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ℵ ϖ ℜ ϒ ℘ ℑ ← ↑ → ↓ ↔ ↵ ⇐ ⇑ ⇒ ⇓ ⇔ ∴ ⊂ ⊃ ⊄ ⊆ ⊇ ⊕ ⊗ ⊥ ⋅ ⌈ ⌉ ⌊ ⌋ 〈 〉 ◊

RELATED TOPICS


Math Algebra 1 Algebra 2 Calculus Trigonometry Probability Algebra Word Problem Proofs Geometric Proofs ... Math Help Triangle Area Circles Triangles Volume Mathematics Midpoint Angles Geometry Word Problems

RELATED QUESTIONS

what is a bisector geomeattempt

Answers · 4

what is an equation equal of a line parallel to y=2/3x-4 and goes through the point (6,7)

Answers · 5

what are some angles that can be named with one vertex?

Answers · 2

name of a 2 demension figure described below

Answers · 6

how to find the distance of the incenter of an equlateral triangle to mid center of each side?

Answers · 6

RECOMMENDED TUTORS


*

Zeth B.

5 (26)
*

Priti S.

5.0 (490)
*

Alexander H.

5.0 (251)
See more tutors

find an online tutor


Download our free app

A link to the app was sent to your phone.

See more: Driving Distance From Kansas City To Denver To Kansas City Drive Or Road


Please provide a valid phone number.
Google Pput App Store
Get to know uns
Learn with us
Work with us
Download our free app
Google Pput App Store
Let’s keep in touch
Tabs over spaces!

Need more convincing?


Best in business since 2005
*
*

Tutors by Subjecns
Tutors by Location
Sitemap Terms of Use Privacy Policy
© 2005 - 2021 rebab.net, Inc. - All Rights Reserved