How to determine the number of sides 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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Organized Videos:
✅Polygons
• Polygons
✅Sum of Exterior Angles of a Polygon
• Sum of Exterior Angles...
✅One Exterior Angle of a Polygon
• One Exterior Angle of ...
✅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
• One Interior Angle of ...
✅Interior Angle Sum of a Polygon
• Interior Angle Sum of ...
✅Interior and Exterior Angles of Polygons
• Interior and Exterior ...
✅Classify Polygons
• Classify Polygons
✅Congruent Polygons
• Congruent Polygons
✅Similar Polygons
• Similar Polygons
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[@Ollurim]

I know this is a very old video, but I still wanted to say thank you. This definitely helped a lot.

[@Boxolotl]

Holy smokes Peter Griffin is in Fortnite

[@megv7481]

that was... something i actually understood, thanks!

[@brianmclogan]

you are very welcome!

[@munaali9439]

Wow that was amazing teaching.

[@floramoayed5316]

Thank you so much, your explanation was much more helpful than others.

[@brianmclogan]

happy to be able to help you out!

[@DarthOtterTheWise]

@@brianmclogan This video saved my life because i forgot how to do this

[@NotNathanH]

Thanks! Im in geometry right now and need to take a test based on this. So this really helped me understand the formula.

[@stultusmus1823]

Wow... i learnt this in 5 minutes! Thank you

[@brianmclogan]

Bam!!

[@air_68]

I love how he is dilebratly avoiding the camera 😂 Thanks!

[@motupatlu5991]

There is a much simpiler way 180-156=24 360÷24=15

[@damsie64]

Can u explain? Sry I don’t quite understand Edit: I don’t understand why u did it this way

[@romelgonzales5829]

Damsie By knowing that the sum of all the exterior angles of a polygon is 360 degrees-- whether it's a regular or not -- he solved for the supplement of the 156-degree angle; he divided the measure of the supplementary angle from 360 degrees to know how many sides there are.

[@simi-ahmad397]

Thanks so much this helped a lot with my homework but also does this work with any polygon or just this one in particular?

[@samarabhikha1010]

@@simi-ahmad397 hii yes it works with any polygon only if it tells your the interiors degrees ((:

[@simi-ahmad397]

@@samarabhikha1010 thanks so much x

[@wrldxm8629]

this may be 6 years old but still helpful thnx

[@sherwinvincentcatubig3427]

Thank You! Big help for my howework

[@anikatabassum6233]

I’ve an easy method Let us consider the regular polygon is 165 degree =(180-165) degree =15 degree =360/15 = 24 Therefore, there are 24 sides for 165 degree

[@swiftie_2247]

sir u saved my life God bless u!!

[@St-jh8pk]

Thank you, this really helped me understand!

[@JackalopeAirlines721]

Thank you! This help me understand my math work.

[@liferacer3967]

Thank you, I was struggling for a while to understand but its all good now

[@essaahmed7744]

thank you soo much very helpful video

[@bhawnajain6564]

The video helped alot......It is the BEST👍👍👍👍👍

[@damsie64]

TYSM!

[@surajsingh9389]

Easy to understand., Thank you sir

[@brianmclogan]

you are very very welcome!

[@cameronglenn5478]

this video saved my life i almost killed myself tryna do my homework

[@Malakfox]

Math is hard but thanks I understand now! :)

[@tekueldruida]

You save my clash of code, thank you

[@lindsay6037]

Thanks a lot!

[@samarabhikha1010]

who knew 8 years later this would still be helping us

[@MeowCowGoPow]

11 …

[@mothquing4990]

does anyone have the formula

[@trinityredford1415]

Is there a flat out formula for this? (180-x)÷360=n x=one interior angle if regular polygon n=number of sides

[@worldsworstgamer7320]

You did have the right idea, but your formula is backward. it should be. 360÷(180-x)=n

[@nukedacat7457]

wait.... your doing number 7 and im doing number 7. hmm, im doing the cambridge igcse 2018 book but this vide was published 10 years ago how in the world does that make sense?

[@antoniocorona2433]

Very helpful

[@brianmclogan]

you are very welcome!

[@motupatlu5991]

Where did u get the 360 from?

[@julianaivie3341]

Motu Patlu i know it’s late lol, but since he had to do distributive property, he multiples both n and 2 by 180, giving him 180°n and 360 instead of n-2(180)

[@biggusrichard1721]

Stop haunting me your example is the same problem i needed help on

[@tiagoferreira8797]

Very sorry .This didn't help me I just ended up getting the answers to my homework from my friends but you did help me a little bit so thank you

[@taaseenmurshed2514]

Thnx

[@brianmclogan]

you are very welcome!

[@Noooooooooooooooooooooo0]

this guy is carrying me through math lol

[@nicoreyes3125]

Can someone tell me y when u do 156n-180n it’s -24n and not -24

[@tenzin7068]

n will always be apart of the number unless it is divided out, it will only be negative 24 if it was 156-180

[@jeffro1245]

why is the sum of the triangle 180 and the sum of the square 360?

[@MeowCowGoPow]

@@jeffro1245 square can fit minimum 2 triangles inside.

[@taraveale1341]

this actually helped me so much

[@brianmclogan]

you are very welcome! happy to help

[@silent3341]

cant still understand sorry sir.

[@hdjejdjdowjefs6830]

I don’t get it

[@victoroditah9403]

I could not understand this at all, it was so confusing and could not finish the questions. 😥

[@brianmclogan]

What is your question?

[@Happy123]

can you explain why is the sum of all interior angles (n-2)x180

[@brianmclogan]

start with a triangle, then rectangle and you will see it holds true for all polygons

[@imranahmed-dp5vt]

good

[@brianmclogan]

happy to help

[@Dark-ds6vr]

its basically 360/180-Interior Angle your welcome

[@afshansajjad7849]

Tgank youooouu

[@brianmclogan]

you are very welcome!

[@fraserlyons1344]

Still Confused

[@fraserlyons1344]

What does the "N" stand for

[@brianmclogan]

the number of sides

[@a1brothers..164]

Me toooo

[@lynd4278]

Ok but in my book the formula is (2n - 4) × 90° 😭😭😭😭😭😭😭😭😭

[@brandonjohan]

It’s just the same formula but not simplified

[@sh4dowxff376]

You don't know cross multiplication