Angles of any shape instantly - By tecmath
Transcript
| 00:00 | Good day . Welcome to take Math Channel . What | |
| 00:02 | we're gonna be having a look at in this video | |
| 00:03 | is a really fast , cool little way of working | |
| 00:06 | out the total interior angles of any polygon . So | |
| 00:11 | I'm going to say that a normal plain english now | |
| 00:13 | , I'm talking about what the total of these angles | |
| 00:15 | inside This particular shape . This is a hexagon , | |
| 00:19 | but any many sided shape , how you can work | |
| 00:22 | that out . So this could be a six sided | |
| 00:23 | shape , like this hexagon here , or it could | |
| 00:25 | be an eight sided shape or it could be a | |
| 00:27 | 10 sided shape or 100 sided shape and how you | |
| 00:30 | can work out what the total of the angles of | |
| 00:33 | the shape is . Okay . And then from that | |
| 00:35 | you can actually see the equal angles , work out | |
| 00:38 | how big each angle is as well . So that's | |
| 00:41 | fairly uh it's a fairly good little trick for doing | |
| 00:43 | that also . So although it straight into how I'd | |
| 00:47 | work on this hex again here , so the way | |
| 00:49 | this works , what we're gonna be having to look | |
| 00:51 | at with this is we're going to be basically working | |
| 00:56 | with this idea which is first off , we're gonna | |
| 00:58 | have a look at triangles in there . You may | |
| 01:00 | or may not know this with triangles . First off | |
| 01:02 | , a triangle has three angles 123 and that these | |
| 01:06 | angles add up to 180 degrees . So that this | |
| 01:11 | angle plus this angle on this angle 100 and 80 | |
| 01:13 | degrees . Doesn't matter on the triangle . The angles | |
| 01:15 | always add up to 180 degrees . So what we're | |
| 01:18 | gonna do is we're gonna break our hex again here | |
| 01:20 | up into triangles . So I'm gonna start from one | |
| 01:24 | of the uh corn and see and one of the | |
| 01:26 | uh one of these points . And we're gonna start | |
| 01:30 | making triangles . Okay , so I have one triangle | |
| 01:34 | , I have two triangles , I have three triangles | |
| 01:38 | . And I have 1/4 round . The lab 123 | |
| 01:41 | four triangles . And so now it's pretty simple . | |
| 01:44 | We do . Each of these triangles is 180°. . | |
| 01:47 | So four Times 180°. . And we will have our | |
| 01:51 | answer . Okay so four times 100 and 80 this | |
| 01:54 | is 720 degrees . So the total of these angles | |
| 01:59 | within this hexagon Is 720°. . Okay so that's pretty | |
| 02:04 | cool . Right um What about , I'll go to | |
| 02:07 | a different shape . What a pair ? We have | |
| 02:10 | a look at the octagon which you probably all know | |
| 02:15 | already has . How many sides ? That's right . | |
| 02:19 | Stateside . So I would get you to draw out | |
| 02:21 | an octagon . Man , that's a bit but ordinary | |
| 02:24 | that bottom or draw that again . Yeah . Okay | |
| 02:27 | . Um I'll get you to draw it out and | |
| 02:29 | get you to try and do this as well . | |
| 02:31 | So I'm going to break this up into as many | |
| 02:33 | trials I can . So we have what draw angle | |
| 02:36 | here ? Two triangles , three triangles , four triangles | |
| 02:47 | , Five triangles and six triangles . Okay so we | |
| 02:49 | have 123456 triangles . Okay so six Times 190 will | |
| 02:57 | give us the total of all of mhm . These | |
| 03:04 | angles cases six times 180 Is 1,080°. . So it's | |
| 03:10 | a pretty cool little trick . Right ? And you | |
| 03:11 | might say well does it work for um different types | |
| 03:15 | of shapes here ? You might not have thought that | |
| 03:17 | . Okay but I'm going to ask that question for | |
| 03:19 | you and answer it for you um to say we | |
| 03:21 | had a pentagon , the pentagon and I wasn't drawing | |
| 03:25 | it particularly nicely , I was drawing it so it | |
| 03:27 | looked a bit like this . Okay , Okay . | |
| 03:31 | uh yeah so it's a 12345 sided shape . Okay | |
| 03:36 | maybe I'll uh just changes a bit to accentuate that | |
| 03:39 | a little bit more . Okay so you'll see here | |
| 03:41 | we've got a five sided shape . Yeah , it | |
| 03:44 | also works for the pentagon that looks like this . | |
| 03:48 | Okay , because I want to do is break it | |
| 03:49 | up into the triangles . Okay , so I have | |
| 03:51 | one triangle here , I have two triangles and I | |
| 03:55 | have three triangles . We have 123 Okay , so | |
| 04:00 | three Times 180°. . This is equal to 500 And | |
| 04:08 | 40°. . Okay so this angle , this angle , | |
| 04:10 | this angle , this angle and this angle Add up | |
| 04:14 | to 540°. . So it's a it's a really really | |
| 04:18 | great little trick for that . And you might even | |
| 04:20 | have your very very good with um algebra or anything | |
| 04:25 | like this or formulas be able to almost put together | |
| 04:27 | a formula for this ? I'll give it to you | |
| 04:29 | if you want to know by the way . So | |
| 04:30 | pretty much the formula for this . And if you | |
| 04:33 | don't like formulas just bear with , because I'm going | |
| 04:34 | to show you one thing after this , the formula | |
| 04:36 | for this , the total of the angles is equal | |
| 04:40 | to the number of the sides . Take away too | |
| 04:44 | Time . So the number of triangles that we get | |
| 04:47 | is always to less than the number of sides . | |
| 04:50 | Okay , so it's an eight sided shape . The | |
| 04:52 | number of triangles we're going to get is six and | |
| 04:54 | it's a 10 sided shape . The number of triangles | |
| 04:56 | we're going to get from that is going to be | |
| 04:58 | eight and we're just times now . 180 . So | |
| 05:01 | that's a little formula you can use for this . | |
| 05:03 | Um Now I'm just gonna show you just one last | |
| 05:06 | little application for this . Well there's other ones too | |
| 05:09 | . But you know , just just one for now | |
| 05:12 | and it's this I say we had I'll go back | |
| 05:14 | to my hexagon . Okay Society , we have my | |
| 05:18 | headaches are gone and because of hand drawn it's not | |
| 05:21 | going to be perfect but pretend it was perfect and | |
| 05:23 | pretend what we had is all these angles were the | |
| 05:28 | same . Okay , so it was one of these | |
| 05:30 | lovely sorts of hexagons like that . Now if that | |
| 05:34 | was the case , we could also then work out | |
| 05:36 | the size of these angles really , really simply because | |
| 05:40 | Well we have six sides and you might remember you | |
| 05:43 | can work that out . We can break that up | |
| 05:44 | into four triangles and four times 180 is 720°. . | |
| 05:51 | Okay . But then what we can do is we | |
| 05:53 | can say , okay , so how big is each | |
| 05:55 | angle ? What we just need to divide that by | |
| 05:57 | the number of angles There are , there's 123456 so | |
| 06:01 | 720 divided by six . And you'll see that each | |
| 06:05 | angle is 120°. . So that's where you can just | |
| 06:11 | take that a little bit further . If you need | |
| 06:13 | to know those particular angles there . Anyway , I | |
| 06:16 | hope you enjoyed that video . It's a really , | |
| 06:18 | really great little trick . So , uh , you | |
| 06:20 | know , use it . Okay . Anyway , any | |
| 06:23 | comments ? Any suggestions ? Any uh , criticisms ? | |
| 06:26 | Let us know . Okay , See you later . | |
| 06:29 | Bye . |
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Angles of any shape instantly is a free educational video by tecmath.
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