How to determine the number of sides of a regular polygon, given one interior angle

👉 Learn how to determine the number of sides of a regular polygon. A polygon is a plane shape bounded by a finite chain of straight lines. A regular polygon is a polygon whose sides are congruent (equal). The interior angle of a polygon is the angle between two sides of the polygon. For a regular polygon, the interior angles are congruent (equal).
The sum of the interior angles of a regular polygon is given by the formula: 180(n - 2) degrees, where n is the number of sides of the polygon. Thus, given one of the interior angles of a polygon, say m, to find the number of sides of the polygon, we solve for n in the equation: 180(n - 2) = mn, where m is the given interior angle measure.
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✅Polygons
• Polygons
✅Sum of Exterior Angles of a Polygon
• Sum of Exterior Angles...
✅One Exterior Angle of a Polygon
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✅Number of Sides of a Regular Polygon
• Number of Sides of a R...
✅Sum of Interior Angles of a Polygon
• Sum of Interior Angles...
✅One Interior Angle of a Polygon
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✅Interior and Exterior Angles of Polygons
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✅Similar Polygons
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[@hcolumbia4520]

My friend came up with this: Take the measure of the interior angle, subtract it from 180. You will get the supplement (exterior) angle of the interior one. Take 360 and divide it by the number you get. So the formula is 360/(180-interior angle). I hope this makes sense to someone, it has worked for every problem I've tried so far but I'm no mathematician so let me know if it doesn't.

[@brianmclogan]

for regular polygons it works

[@ayowandeadeoti8170]

Thank you sooooooooooooooooooooooooooooooooooooooooooooooooooo much. I watched the video and I understood it a bit and then I read your comment and it worked with all my questions. I have my end of year maths exam tomorrow ans this will help me a lot. thanks again

[@Jeffozzz]

Thanks Holy roscoe

[@myeshachoudhry967]

hcolumbia- yeh it rlly does work rlly easy way of calculating Thnxs

[@ameliachalk2029]

I love you so much!!!!! Thx 🙏

[@brianmclogan]

Sweet, I will be posting all year, just let me know how I can help you out

[@bloab]

The sides of this polygon subtend angles of 18° at the centre of the polygon. how many sides does it have? how do i do this?

[@Lanachick]

Pleas 2+6

[@vyankteshingole3458]

@@Lanachick hey its 8

[@maryjoypernia6451]

Thank you for teaching now i understand what my teacher teaches me

[@arda8917]

Exam rn thanks soooo much

[@brianmclogan]

you are very welcome!

[@tarr7784]

The teacher looks concerned when the students cant answer his question

[@collinstacy5561]

My teacher does the same lol

[@jimharris8854]

Awesome. Thanks for this, my daughter missed a lesson due to covid and this was what she missed! Thanks so much for being so future thinking in uploading this!

[@natevideos263]

Thank you, this channel is great. Keep it up.

[@natevideos263]

Although it would be useful if you wrote the problem on the board as it appears on the worksheet.

[@mariannegarlicki3580]

This is helpful to a parent who has not done geometry in a long time, thank you.

[@brianmclogan]

you are very welcome Marianne!!

[@thehikingcamera]

Thank you so much for this video! Our teacher just gave us this worksheet without telling us anything.

[@phantomreal1425]

I have been given set angles for homeschooling but they don’t teach it they just give and expect you to know it so this video has just helped me. Thank you

[@dude6697]

was stuck on an assignment and i watched this and all the pieces clicked in my head

[@bhowanyreena2852]

Thank you sir

[@thusharanup4906]

You have a real knack for teaching :) thanks a lot!

[@brianmclogan]

you are very welcome!

[@ZyfoAI]

bro you are the best

[@medicmayhem1]

Thank you, the online classes im taking are awful and didn’t actually tell me how to do the problems so this was very helpful, thank you

[@twincrown2850]

Thank you very much. It helped me alot.

[@dailymeme4u]

Thnx for this sir. It will help me in my final exam

[@sandeeps7625]

thank you so much sir

[@horjamorja6852]

What an awesome teacher fr

[@calimaxamed111]

Thank you very much. I have a question about the formula ☝️☝️ Sum ( n - 2 ) 180. n stands number of sides. What 2 stands? Where 2 is come from?

[@saarahahmed585]

Im from the UK and have my last math calc paper tomorrow! Wish I found your channel sooner- thanks for the help!!!

[@brianmclogan]

you are very welcome! best of luck

[@luketownsend3861]

Thank you so much man this really helps me a ton I wish you were my actual teacher

[@brianmclogan]

Luke Townsend awesome! happy to help, still making videos but not teaching Geometry this year, hopefully next

[@roguewipplash1]

thanks very helpful

[@Pokefreakxs]

thanks a lot!!

[@brianmclogan]

you are very welcome!

[@zeshukitagora7694]

pretty hard but after 3 times of watching i finally got it thanks

[@brianmclogan]

you are very welcome!

[@eviebonner4674]

Thank you, you explain so well

[@mousaalqarizi6401]

Thank you a lot Mr. This was helpful to me, especially the interior angle formula.

[@brianmclogan]

+MOUSA ALQARIZI awesome! happy to assist you

[@shmittybacall1499]

Your a saint my good man

[@trezerbeats]

Thank you so much, helps me a lot :)

[@brianmclogan]

you are very welcome, happy to help

[@cristinabautista2547]

Thank you!. this what i looking for

[@mohummadkashif2336]

thank you sir it helped a lot you are the only reason that i can freely sleep in my math class as my first class every day is my math class and i am very sleepy during the class

[@shahwarbasith2295]

THANK YOU! I FINALLY FINISHED MY IXL BECAUSE OF YOU! YOU THE MAN!

[@brianmclogan]

you are very welcome!

[@07jas]

This was so helpful!!

[@milomansour865]

Holy thank you so much I have a test tomorrow and I have no idea what to do for this part thanks

[@nabhanya]

Thank you so much!!

[@muhammadsachalofficial5470]

Awesome it taught me everything to know 😃

[@movlogs8467]

you are the absolute best love you

[@mimi-iy7jv]

thank u this helped a lot, ur a very good teacher, also what would be the equation for solving an exterior angle instead

[@brianmclogan]

just divide 360 by the number of sides

[@timothydelrosario100]

Good thing this video popped up because in my math book, they expect YOU to know the steps already so u can do it so the explanation in my book is completely unclear, but in this viedo, it made actual sense than my book, thx logam

[@timothydelrosario100]

Logan* typo

[@brianmclogan]

+Timothy Del Rosario that's why I love teaching on youtube! happy it helped you

[@brianmclogan]

+Timothy Del Rosario no worries

[@moazelmasry6988]

your a legend my guy keep it up!

[@lyle.justin.stoffels]

Oh sweet baby Jesus, THANK YOU!!!

[@brianmclogan]

Lyle Stoffels you are very very welcome!

[@zleepyjan]

thank you

[@channabiryan]

Thank you soOoOO much!!

[@10Epochs]

thx its helpful

[@brianmclogan]

you are very welcome Ayush!

[@stanslousngugi5510]

thx it helped alot😁

[@yahirgarduno2514]

Nice video teacher

[@Deepakdeepak-ur5xq]

Thanks this helped me a lot

[@kiwidominecraft4956]

Helpful! Thanks

[@brianmclogan]

you are very welcome! happy to be able to assist you

[@NH-gt8un]

Thank You!

[@brianmclogan]

you are very welcome

[@gomba3987]

thank you mista

[@adilazher4168]

Thank You very much!!!!!! This helped a lot.

[@brianmclogan]

awesome! happy to help

[@sarmilachhetri5976]

Thanks sir😮

[@itsnotrhenlopez7626]

thank you sir..for a great video...now i know the formula...thnks for helping us more power to you....

[@brianmclogan]

+Jhen Dela Rosa you are very welcome! happy to be able to assist you

[@m.tloz5]

Thank you Sir for making these videos. They have really helped me in school !

[@rohinvfx]

man thx you helped me alot and earnt a sub

[@shaunvilla3181]

Thank you, I needed to know how to solve this for a test I have tomorrow . You’re a life saver🙏🏽

[@hailweb-b8t]

same bro

[@fernandowong2346]

How if the question ask to find the number of sides of a polygon where each its interior angles is 120 greater than each exterior angle of the polygon? I'm confused

[@sharvinraj8232]

Thanks man...You helped me in my exam..Thank you...

[@brianmclogan]

+Sharvin Raj you are very welcome! happy to help

[@mohamedfaisal6991]

help me with bearings please if you got a time to do and make vidoe for that particular lesson.

[@olichapman6053]

Thanks bro

[@swayamnath7018]

Thank you for helping me out with this thing

[@brianmclogan]

you are very welcome!

[@swayamnath7018]

Gracias

[@catboykay]

thanks mister :)

[@Walrus931]

Thank you THANK YOU THANK YOU! You are mini Jesus

[@anthonychuakianbeng2081]

OMG U HELPED ME

[@MelissaJoans]

I actually forgot how my class did it (Since it's a bit different), but this video was helpful because I have an upcoming exam in some weeks. Thanks!

[@brianmclogan]

you are very welcome Lisa! best of luck on your exam

[@karmabliss2002]

Ok, well I hope so. But my friend explained it to me and your method sort of made sense if that's any consolation.

[@brianmclogan]

+Karma Lazzeri I'll take it! happy to help

[@thealleycat_5741]

THANK YOU SO MUCH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@brianmclogan]

Kisa Sohma you are very welcome! happy to be there to help you out!

[@alihaidar9744]

There's a much simpler method. find the exterior angle then divide by 360. For example, 180-108= 72. Then 360/72 which will give you the number of sides, in this case it's 5.

[@brianmclogan]

correct, I have other videos that explain that way as well

[@alihaidar9744]

Brian McLogan alright, thanks for the clarification, just thought my method would be faster during exams etc :p

[@izaan.ala2]

you are truly a legend my friend

[@joshthelad1721]

Thanks

[@brianmclogan]

you are very welcome!

[@sherwinvincentcatubig3427]

Thank Youu!

[@henrykahue1780]

Thanks mayn, the struggle was real into I saw this video

[@brianmclogan]

hahaha happy to help

[@nathan6288]

Thx for the help, you're the best. 😂😂

[@sumeragi8855]

is it possible for an interior angle and exterior angle of a irregular polygon to be congruent?

[@brianmclogan]

of course, for regular only a rectangle or square work

[@uoyebut8953]

U r the best

[@brianmclogan]

Happy to help!!

[@uoyebut8953]

@@brianmclogan continue to do so👊atleast until i finish highschool😂

[@deathorock3995]

thanks for the video I needed it fr

[@brianmclogan]

no worries

[@pseudonymphmusic7721]

Thank yousoooooo much

[@brianmclogan]

+brianna brady you are very welcome! happy to be able to help you out!

[@toddbaket3537]

Really appreciate the help from this video!

[@brianmclogan]

you are very welcome!

[@naturistic2970]

👍👍👍👍 awesome

[@bloab]

The sides of this polygon subtend angles of 18° at the centre of the polygon. how many sides does the polygon have??

[@NiloyDas-hb3jg]

One of the best math videos I've seen, honestly. Thank You, earned a subscriber

[@brianmclogan]

you are very welcome! happy to have you

[@zanesewell3174]

exam tomorrow thank u!!

[@swayamnath7018]

I love it

[@brianmclogan]

: )

[@tiarailic4086]

So what I don't super understand. I have a problem almost exactly this but different numbers so when I came to this step. 162n=180n-360. So I subtract 180 from 180 and 180 from 162 . I ended up getting the right answer (I think) but why would you subtract 180? Wouldn't you divide since 180 is being multiplied with n?

[@brianmclogan]

yes but when solving equations you have to get the variables on the same side first. for example take a easier problem 5x=2x-6 to solve this problem you will subtract 2x on both sides to obtain 3x=-6 Now you can divide by 3 to solve

[@tiarailic4086]

Thnks:) my Dad helped me with it. He's a math wiz:)

[@anasgardengnome9602]

never knew arjen robben was good at maths

[@brianmclogan]

haha

[@anasgardengnome9602]

on a serious note tho that was a quality video thank you for uploading it :)

[@mohamadarrifin8678]

Thanks mate

[@brianmclogan]

cheers!

[@queeno9010]

Wow taht was sick but I still don’t get it do u have an easier way I get it but I might not remember it in the exams

[@snehalatakhopde3149]

Good...

[@titalinda3136]

Count the number of sides of coch polygon and closely what type based on its number of sides.

[@steflondon88]

thaaaaaank you

[@brianmclogan]

you are very welcome!

[@emilyhadley4670]

if you subtract by 180n how does this not cancel out the n?

[@brianmclogan]

+Emily Hadley because the n and terms are separated by subtraction, you have to divide both terms by n for instance (4+8)/4 =3 not 8

[@sxdium_8213]

Damn u better than my teacher

[@iceyygirl.mp4684]

How’d you get the -72n

[@rolasca5494]

How do I work out the number of sides of a regular polygon when the interior angle is 156° ?

[@brianmclogan]

need to use the formula for interior sides of a regular polygon

[@hamzajaved6379]

156n - 180n = -360 -24n = -360 n = 360 divided by 24 n = 15

[@blazingjalapeno9096]

My teacher didn't even teach is this and he gave these type of problems to us >:(. Thank you for this video

[@brianmclogan]

you are very welcome!

[@zaidmuhammad7783]

i got a sum here need help how do i workout if the interior angles add to 1140

[@brianmclogan]

same as the video, divide the sum by the number of sides, to find the number of sides use the process in the video

[@dafnesanchezcuesta6865]

I didn’t understand why does it equal 5 at the end, how do you get to that?😩

[@vocabified]

awsum sir 😆

[@brianmclogan]

happy to help

[@joysarkar3772]

nice

[@brianmclogan]

thanks!

[@hamzajaved6379]

I wish he was my sir