Naming & Measuring Angles in Geometry with a Protractor - Part 1 - [3] - Free Educational videos for Students in K-12

Naming & Measuring Angles in Geometry with a Protractor - Part 1 - [3] - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called naming and measuring angles . This is part
00:05	one . So what we first want to do is
00:07	teach you and understand how to name an angle .
00:10	So we write the name of the angle down .
00:12	We all know what we're talking about . And secondly
00:14	we're now we're going to start to talk about how
00:16	to measure angles . So first let me talk about
00:18	the measure measurement part first . Remember we want to
00:21	measure an angle , we want to find out how
00:23	open the angle is or how closed it is .
00:26	That is what the measure of an angle is .
00:27	And if you open it all the way up 360
00:30	degrees , that's a full circle , anything less than
00:33	that is going to be less than 360 degrees .
00:35	We talked about that , we talked about right angles
00:37	, acute angles and obtuse angles . Now to measure
00:40	angles . We're going to use this thing called a
00:41	protractor and you might have one of these . If
00:44	not , you probably should get one , but I'm
00:46	going to draw my pro tractors out so you can
00:48	kind of see before we do that though . Let
00:50	me just draw a general angle here . So we
00:53	know that this angle is going to be bigger than
00:55	zero degrees . If this ray , we're all the
00:57	way down here on top , it would be not
00:59	open at all , it would be zero degrees ,
01:01	This is 90 degrees and then here is bigger than
01:04	90 degrees . Now in order to measure it ,
01:06	you take this device and there's usually a hole or
01:10	a notch in the center and you put it where
01:12	the to raise come together , you put that kind
01:15	of right in the hole and then you line up
01:18	one of the rays with the device here . And
01:21	then what you do is you look at where the
01:23	other ray kind of cuts into it and you read
01:26	the measurement right off of the protractor . This is
01:29	called a protractor . So you put the the where
01:31	they come together , what is called the vertex where
01:34	they come together by the way in the center line
01:36	up one of the raids like this . And then
01:37	you just read the measurement right off . Now .
01:40	It's really , really hard to read this protractor um
01:43	because it's so small . So what I've done over
01:45	here is I've redrawn the protractor for it so we
01:48	can all be on the same page . So now
01:50	what we're going to do now , you know what
01:51	we're kind of doing is we're going to take a
01:54	look at an angle and we want to measure it
01:56	. Here is an angle I have now labeled it
01:58	where the beat . There's a letter B in the
02:00	center . We call it the vertex and then we
02:03	have the letter C . At this dot in the
02:05	letter A . Here . So here's how we're going
02:07	to name an angle . We're gonna say the angle
02:09	measure is equal to something . We're gonna write it
02:11	down . So what you first do is you write
02:14	this little symbol here , This little this little angle
02:17	looking thing with a kind of like a curve through
02:19	it . This symbol means angle . That's what it
02:21	means . It means angle . So this symbol means
02:24	angle uh angle which name will follow . And the
02:28	name of this angle is called angle A . B
02:32	C . Why is it called abc ? Because notice
02:35	it follows . A . Is here be is that
02:37	the vertex in the center and see is way over
02:39	here . That's the way you want to name the
02:41	angle . You could name it backwards if you want
02:44	. It could be named abc . It could also
02:47	be named angle C . B . A . Either
02:50	order is okay , but you have to make sure
02:53	that the letter B . Is in the centre because
02:55	B . Is where the rays come together , it
02:57	has to be in the center . So here we're
02:59	gonna call this angle abc . And of course you
03:02	could say C . B . A . If you
03:03	want to , but we're gonna call it A .
03:04	B . C . And now we have to come
03:05	up with a measurement . Now we know that this
03:08	uh if this will ray this right here and then
03:10	we had this , if this one were over here
03:12	, it would be a 90 degree angle B .
03:14	A . Right angle but it's not . So let's
03:16	put a protractor on top and that's what we have
03:18	down here . We have the exact same angle .
03:21	Notice A . B and C are here . Now
03:22	we put a protractor on top . What we want
03:25	to do is measure how open it is from this
03:27	ray . All the way to here . Notice that
03:30	if we go straight up from here , then you
03:32	can see a 90° mark . It might be hard
03:34	for you to read here , but this is 90°
03:36	straight up and down . And then all of the
03:38	numbers bigger . This is 100 degrees 110 degrees and
03:41	so on . I want you to ignore for now
03:44	ignore these outer numbers only look at the blue numbers
03:46	here . We know that the angle measure has to
03:49	be bigger than 180 because remember a right angle is
03:53	90 degrees . But this is larger than that .
03:55	It's more open . So it has to be an
03:57	angle measure bigger than 90 . So all you have
04:00	to do is look where this thing cuts and you
04:02	have a choice is it going to be 20 degrees
04:04	or is it going to be 160 ? It has
04:07	to be 160 because we know that it has to
04:09	be bigger than 90 degrees right here . So we
04:12	say that the measure of angle abc is equal to
04:15	160 you put a little degree mark here . This
04:19	symbol means degrees . Now you might say why do
04:22	we have to scales here ? Okay . The reason
04:25	is because if we're measuring this angle here , we're
04:28	going to pick the big number , 60 degrees .
04:30	That's this number . But if we have this angle
04:32	here and instead we're measuring from this angle down to
04:35	this horizontal line here , that's 20 degrees . So
04:39	you basically want to ignore the 20 because we're always
04:41	interested in the angle between the rays . So basically
04:45	, you know , straight up and down his 90
04:47	smaller angles have numbers smaller than 90 . Their acute
04:50	larger angles have angle measures bigger than 90 . They
04:54	have to be obtuse . So when you look at
04:56	the Ray , you have to choose the correct number
04:58	. And we know it has to be 160 because
05:00	it has to be bigger than 90°. . Okay ,
05:04	all right , next here we have an angle .
05:08	We have J . K at the vertex and L
05:11	. So we're going to name this guy angle .
05:14	That's the angle symbol J K L . We have
05:18	to make sure K is in the centre because it's
05:20	at the vertex and it's in the center between those
05:23	points . So we're gonna call that J K .
05:25	L . And now we have to measure this .
05:27	So here we have J K . L again .
05:30	And we want to measure how open the angle is
05:32	. See from this race straight up . It would
05:34	be 90 . But this has to be bigger than
05:35	90 because it's more open than that . So our
05:38	choices are 50 or 1 30 . What is the
05:41	angle measure ? Have to be has to be bigger
05:43	than 90 . So it's 130 degrees . 130 degrees
05:48	. 130°. . You can ignore the 50 . The
05:51	50 is here . If you were measuring this down
05:53	uh down to this spot here , that would be
05:56	a 50° measure . But we're not measuring that .
05:58	We're measuring the big angle . We know it has
06:00	to be bigger than 100 than 90°. . So it's
06:03	130°. . Alright problem number three . We're gonna measure
06:09	this angle . How do we write it down ?
06:11	Q . Has to be in the center . So
06:13	we put our angle measure P . Q . R
06:17	. P . Q . R . And now ,
06:20	what is the angle measure itself gonna be ? Let's
06:22	take this angle and let's put a protractor on top
06:24	of it . Who are measuring how open this angle
06:27	is now ? This is 90°. . So this is
06:29	way less than 90 . So we have to choose
06:31	between 40 degrees or 140 degrees . And we know
06:35	the angle measure has to be less than 90 because
06:37	it's a cute . So the answer has to be
06:40	40 degrees 40 degrees . Now you might say ,
06:45	well , what are these other numbers for that is
06:46	if I was measuring this ray , The angle from
06:49	it all the way over here . That is the
06:52	angle measure called 140° from here to here . But
06:55	we're not measuring that . We know the angle has
06:57	to be a small number because it's a cute .
06:59	It has to be less than 90°. . All right
07:03	. Let's take a look at this angle here .
07:05	We have Y at the vertex that's at the center
07:08	X . And zero on the other side . So
07:11	we're gonna call this angle X , Y . Z
07:15	. Y has to be in the middle . Remember
07:16	? We could call it Z . Y X .
07:18	If we want . But we have to have why
07:20	? In the center ? We're gonna call it angle
07:21	X . Y . Z . What is the measurement
07:23	of this angle ? Let's take a look down here
07:25	. It's lined up on the protractor and you can
07:27	see this is horizontal and this one cuts right through
07:31	90 degrees . In fact , both numbers say 90
07:33	. So , the angle measure here is exactly 90
07:37	degrees now , because we now know from the protractor
07:41	, it's exactly 90 degrees if we wanted to .
07:43	We could come over here and put that little square
07:45	in the corner Because that tells me that tells the
07:48	reader that that angle measure is exactly 90 . We
07:51	didn't know that ahead of time until we measured it
07:53	. But now we do . So we can add
07:54	it if we want to now notice that both numbers
07:57	say 90 . That means the angle measure this way
08:00	is 90 . And it also means the angle this
08:02	way to the horizontal is also 90 because You've kind
08:05	of taken this and cut it straight in half .
08:07	So this is 90 and then this is 90 .
08:08	That's why the numbers are exactly the same . Yeah
08:13	. All right . Let's take a look at problem
08:15	five . What angle do we have here ? We
08:18	have F in the middle . We're gonna call it
08:19	G F E . We're gonna call it G G
08:23	F E . Or you can call E F G
08:25	. Let's do it that way . Just to have
08:26	some variety . We'll call it angle angle E .
08:29	F . G . The only thing is you have
08:32	to have F . In the middle because that's at
08:34	the vertex at the point there . What is that
08:36	angle measure here ? We have a protractor . This
08:39	is the horizontal . We want to measure this angle
08:41	between these two race . We know that this is
08:43	90°. . So this angle measure must be smaller because
08:47	it's more closed . So we read the two numbers
08:49	. Is it 70 ? Or is it 110 ?
08:51	It has to be less than 90 . So it
08:54	has to be an answer of 70°. . It doesn't
08:57	matter if the angle opens this way or opens this
09:00	way or opens this way . All we care about
09:02	is the kind of how spread those those rays are
09:05	. That's all we care about . And we know
09:07	that when they're spread exactly up and down like this
09:09	it's 90 . So this number has to be less
09:12	than 90 . That's why we pick the 70° measurement
09:16	. And finally we have this angle measure . What
09:20	do we have here ? We could call it T
09:22	. U . V . Or we could call it
09:23	V U . T . Either way is fine .
09:26	So we'll call it angle T U . V angle
09:30	measure T . U . V . What is the
09:31	measurement here ? We read here . This is the
09:34	measurement between this ray And then this one . Now
09:37	we know straight up and down would be 90 .
09:39	This is bigger than 90 because it's more open .
09:41	So we choose between 100 or 80 and so it
09:44	has to be bigger than 90 . So we're gonna
09:46	say it's an angle measure of 100° which is slightly
09:50	bigger than 90°. . So in this lesson we have
09:53	learned how to name angles . We also snuck a
09:56	little bit of learning about what a vertex is .
09:59	The point here . The vertex here is you .
10:02	The point here . The vertex here is why anytime
10:05	you have an angle formed the point there in between
10:08	the race that's called the vertex of the angle ,
10:10	right ? That's a word that we're going to use
10:11	more and more as we go on here . And
10:13	we learned how to name these things and then we
10:15	learned how to use the protractor and we learned how
10:17	to read the correct number off . We know that
10:20	this is open bigger than 90 . So we have
10:22	to pick the 100 degree number . What does the
10:24	other number mean ? The 80 degree number ? That
10:26	is if we were measuring from here down this way
10:29	, This is smaller than 90°, , so it's 80
10:31	. But the number that we care about is between
10:33	the rays , so we have to know if it's
10:35	acute or obtuse . That's why we learned what acute
10:38	angles were in obtuse angles were in the beginning .
10:41	So make sure you can do this . Practice yourself
10:43	. Follow me on the part two . We'll get
10:45	a little more practice .

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Naming & Measuring Angles in Geometry with a Protractor - Part 1 - [3] is a free educational video by Math and Science.

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