Angles in Triangles - Free Educational videos for Students in K-12

Angles in Triangles - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Mouth channel . What
00:02	we're going to be having to look at in this
00:03	video is angles in a triangle . Okay , nice
00:07	, simple sort of video where we're just going to
00:09	look at first off the properties of triangles in terms
00:12	of angles and how to work out unknown angles associated
00:16	with triangles . Okay , so let's launch straight into
00:19	this . So first off , no matter which triangle
00:22	we look at , I'll draw one up right now
00:23	. So no matter which triangle we look at All
00:27	triangles have the following property and that is that their
00:30	angles add up to 180°. . What this means is
00:36	that this angle plus this angle plus this angle all
00:40	add up to 180°. . Okay , so this is
00:44	really handy . We wanted to work out . First
00:46	off , the first type of question you'll get with
00:49	our triangles , which is this . So say we
00:52	have a couple of no one side . Say this
00:54	1 73 degrees and this one here is 42 degrees
00:58	and you are asked to work out the unknown side
01:02	. Well , this is really simple because we know
01:05	all these angles will add up to 180 degrees .
01:09	And so therefore what we need to do is we
01:12	just need to work out what number we need to
01:15	put here to add all these numbers up 200 degrees
01:17	. Okay , so we get 100 and 80 we
01:19	take off 73 We take off 40 to what we
01:23	have left will be the size of the angle .
01:26	So ah 72 and 43 is going to be 115
01:33	. So we get 180 takeoff 15 . We are
01:36	left with An angle of 65° because 65 and 115
01:44	Add up to 180°. . So x here Is 65°.
01:51	. So this is a really , really handy thing
01:54	for working at Tribals straight away with only two minutes
01:59	in . We've already worked out that first thing .
02:01	Uh the next thing I'll show you with triangles ,
02:03	is this okay ? So say we have a different
02:06	type of triangle and this time what we have is
02:10	we have one of these type of triangles , which
02:13	is , I'll show you It's not going to be
02:17	a perfect drawing here . We have this type of
02:19	triangle where this angle here is 70°. . Uh and
02:25	we know that these two side thinks the same and
02:28	we wish to know this angle we wish to know
02:31	. I'll label this angle is slightly different . We
02:34	wish to know angle B . I see . We
02:39	wish to know this angle here . Okay , so
02:42	how do we work this out now ? Because this
02:45	triangle here Is what's known as an isosceles triangle .
02:50	That is , it has two equal sides as denoted
02:53	here . We can also say that this angle down
02:56	here is also 70° this angle and this angle will
03:01	be equal . So now we can use this idea
03:04	of 100 and 80 degrees being the total of the
03:06	angles and we take off this angle and this angle
03:10	we take them off for 70 and 70 is 100
03:12	and 40 will take that away . We are left
03:15	with 40°. . So this angle here is 40 degrees
03:23	. Very good . Okay , let's have a look
03:26	at another thing with triangles . Okay , and this
03:29	is now getting into exterior angles with triangles , interior
03:33	and exterior angles . So I draw this triangle here
03:36	. Uh here we go . 12 three sides and
03:42	oldest label just a couple of angles in this .
03:45	Their first off , just a couple of things .
03:48	What we do is these inside angles . These angles
03:51	inside the triangle . We call interior angles . I'm
03:54	going to label them A . B . And see
03:57	so A B and C . Here are what we
04:00	term interior angles . They are inside the triangles A
04:05	. B . And see now . What we can
04:09	do is we can extend the line of one of
04:12	the sides of the triangle to create an exterior angle
04:16	. Okay , I'll show you the man . So
04:17	I'm gonna extend the line Bc here . I'm gonna
04:19	extend its going along along along along along and extended
04:22	outwards this way . And you'll notice that I formed
04:25	this particular angle here . But I do that .
04:28	I'm going to call this angle D . And this
04:30	is an exterior angle . It's outside the triangle and
04:34	exterior angle . That's angle D . Now there's a
04:38	couple of properties here that are really handy when we
04:41	want to work out unknown angles of this particular triangle
04:46	. We get shapes on this to work out .
04:48	And that is this the first off is this the
04:52	exterior angle that it's D . Here ? And the
04:54	interior angle next to it add up to 180 degrees
04:59	angle D . Here , and the angle next to
05:01	it . The interior angle see add up to 180
05:04	degrees . Nothing surprising because this along here is a
05:08	line And the straight line angle is 180°. . But
05:11	I'll just write that down . So angle see here
05:16	plus angle D . Equals 180°. . Okay . And
05:27	there's another property here that is also handy . Which
05:30	is this , so that's one of them . The
05:32	second property which is really handy for working on unknown
05:34	sides as this . That's the sum of the two
05:37	interior opposite angles from the extra angle . That is
05:39	angle B . And A . Here some of them
05:42	. So we add them together . They add up
05:45	to the same as the exterior angle over here .
05:48	Okay , so angle I plus Angle B . The
05:55	two opposite interior angles add up to the exterior angle
06:00	, so they add up to angle day here .
06:03	Okay , so this is really handy for working out
06:06	a couple of types of questions that you can get
06:08	when you are working with angles of triangles . And
06:12	I'll give you an example of this . So say
06:14	get rid of all this to say I was to
06:16	have the following example , say I'll draw up something
06:19	very quickly uh And we'll work out the unknown sides
06:24	. So say I had this particular shape here and
06:27	I have a few angle sides that we know .
06:30	We have this one which is 120°. . We have
06:35	this one which is 82 . We have this one
06:39	down here which are colored green which is X .
06:44	And we have this one which are color up here
06:46	a different color , which is why . Okay ,
06:49	that's not very clear . I just do that again
06:51	. Ah cool that why ? And so now you
06:55	want to work out these unknown side and we can
06:57	use this idea to do this and I'll show you
06:59	how okay you might be able to go right ahead
07:01	of me and work it out . So the first
07:02	one I'm going to work out the easiest one is
07:05	angle Xia . Okay , so angle X is equal
07:10	to , well , angle X Plus 120° is going
07:16	to equal 100° because this Exterior angle plus the angle
07:21	closest to it add up to 100°. . So we
07:24	have to look at it . We think well If
07:26	we get 180° , Which is what they add up
07:29	to them , we take off this 100 20° of
07:31	the exterior angle we're left with Angle Xia . So
07:36	this is 60°. . So that's the first one .
07:40	Really , really simple . Right ? Oh just rubber
07:45	That part out there and I just put 60° here
07:47	just to help us now . So now we want
07:50	to work out what why is here ? So why
07:53	degrees we're working on that is well this is fairly
07:57	simple because we have we know that all the angles
07:59	here have to add up to 180 degrees . Okay
08:03	, this and this and this ain't all these interior
08:06	angles add up to 180 degrees . So I'm going
08:10	to get 180 degrees and I'm going to take away
08:13	the sum of 82 and 60 . So 182 and
08:18	60 equal 142 . So I'm gonna take that away
08:22	142° and I'm left with 38 degrees . So anyway
08:30	, how's that ? That's really mostly what you need
08:33	to know when you're trying to work out the unknown
08:35	angles within a triangle in that geometric sort of sense
08:38	like this . Okay , Sorry . Hopefully you found
08:42	this video helpful . We will get on to some
08:44	more stuff with geometry and future videos and I hope
08:47	to see you then . Bye .

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