Math Antics - Angles & Degrees - Free Educational videos for Students in K-12

Math Antics - Angles & Degrees - By mathantics

Transcript


00:03	Uh huh . Hi , welcome to Math Antics .
00:08	In our last geometry video , we learned some important
00:11	things about angles . One of the things we learned
00:13	was that angles come in different sizes . Some are
00:16	big and some are small . Well in this video
00:19	we're going to learn how we can tell exactly how
00:21	big or small and angle is . We're gonna learn
00:24	how angles are measured . You probably already know a
00:27	lot about measurement like how you measure how long something
00:29	is with a ruler or a tape measure and the
00:32	units you would use would be inches or centimeters or
00:35	something like that . Right ? But when it comes
00:37	to angles we can't use a ruler to measure them
00:40	or use units like centimeters . And that's because angles
00:42	aren't about length , angles are about rotation . And
00:45	to measure how much something is rotated . We use
00:48	a special unit called degrees . Now hold on a
00:51	second . I thought degrees were used to measure how
00:54	hot or cold something is . You know like it's
00:57	100 degrees outside today . Ah Now that is a
01:01	good point , you smart looking fellow . The word
01:03	degree is used for a lot of different things so
01:06	it can be a little confusing sometimes it makes more
01:09	sense if you just think of a degree as a
01:12	small amount of something . For temperature , a degree
01:14	is a small amount of heat , but for angles
01:17	a degree is a small amount of rotation . And
01:20	there's a special math symbol for degrees that we use
01:22	instead of writing the word degrees over and over again
01:24	, it's this little circle that you put after the
01:27	number and up near the top to see how we
01:30	use degrees to measure angles . Let's get to raise
01:32	that point in exactly the same direction . Then let's
01:35	put one ray directly on top of the other one
01:38	. So it looks like there's only one way there
01:40	, even though there's really two . Now let's take
01:43	the ray on top and rotate it just a tiny
01:45	amount . Counterclockwise , this point on the ray will
01:48	be our axis or centre of rotation . It's just
01:51	like the point at the center of a clock that
01:53	stays stationary while the hands rotate around it are raised
01:57	. Now form an angle that measures one degree and
02:00	as you can see one degree is a really small
02:03	angle . We need to zoom in on it to
02:05	see that it really is an angle . In fact
02:07	you might wonder if there could be any angle smaller
02:10	than one degree , yep . There Sure are .
02:13	And we saw one just a second ago before we
02:16	rotated our top ray when are rays were exactly on
02:19	top of each other . That was a zero degree
02:21	angle and there's a whole range of tiny fraction angles
02:24	in between zero and one degree . But we aren't
02:27	going to learn about them in this video instead ,
02:30	we're going to keep on rotating our top ray and
02:32	watch the angle get bigger and bigger . This special
02:35	readout here will tell us how many degrees are angle
02:37	measures . Now let's start out slow . One degree
02:40	, 23456789 and 10 . Now let's hold it there
02:47	for a second . So this is what 10 degrees
02:49	. Looks like 10 degrees . That's for freezing .
02:54	Huh ? Guess you're not as smart as I thought
02:56	after all , so we can see that a 10
03:00	degree angle is still a very small angle . So
03:02	let's keep going but a little bit faster this time
03:05	. Alright , that's 15 degrees . 2025 30 35
03:10	40 and 45 . Now , 45 degrees is a
03:13	special angle because it's exactly half of a right angle
03:17	. If we draw a right angle in the same
03:19	spot , you can see that a rate cuts it
03:21	into two equal parts . So if 45 degrees is
03:25	half of a right angle , can you guess how
03:27	many degrees or right angle is ? Let's keep on
03:30	rotating to see if you're right 50 60 70 80
03:34	and 90 yep . A right angle is exactly 90
03:38	degrees and that is super important to memorize because right
03:41	angles are used all the time in geometry . Okay
03:45	, do you remember from our last video that all
03:47	angles less than a right angle are called acute angles
03:49	? So that means that all the angles we've seen
03:51	so far that are between zero and 90 degrees ,
03:54	like 10 30 45 60 and so on . Are
03:57	acute angles . But if we keep on rotating are
04:01	a past 90 degrees will start forming on two singles
04:05	because they're greater than a right angle . Ready here
04:07	we go . 100 degrees . 1 10 , 1
04:11	21 31 41 51 61 70 and 1 80 .
04:17	Ha ha does this look familiar , yep , it's
04:21	a straight angle like we learned about in the last
04:23	video , the rays point in exactly opposite directions and
04:27	the angle they form is 100 and 80 degrees and
04:30	that's also a really important angle measurement to memorize .
04:33	Now , before we go on , let's quickly review
04:36	the important angles and regions that we've looked at so
04:39	far , Our angle measurement is 0° when the rays
04:42	point in exactly the same direction , It's 90° when
04:46	they're perpendicular and form a right angle and it's 180°
04:50	when they point in opposite directions and form a straight
04:52	angle In this region between 90 and 180 we find
04:57	up to singles And in this region between zero and
05:00	90 we find acute angles . One important acute angle
05:04	is 45° since it's half of a right angle .
05:07	All right then let's continue rotating past 180° are angle
05:12	readout keeps getting higher . And the next important angle
05:15	we come to is this 1-270°. . It also forms
05:19	a right angle , but it points down instead of
05:21	up . Let's keep going because another really important angle
05:25	is just around the corner and it's coming up right
05:28	about . Now we rotated are ray all the way
05:31	around the axis and now it's back to where we
05:33	started . Now you might be wondering if we're back
05:36	to where we started , then why is our counter
05:38	reading 360 degrees instead of zero degrees like before ?
05:42	And the answer is that even though our rays are
05:45	back to the same place , we had to rotate
05:47	our top rate 360 degrees to get there . And
05:51	you can see that our angle arc now forms a
05:53	complete circle . So 360° is the angle that represents
05:57	a full circle , Rotating 360°, , brings you all
06:02	the way around the circle to the point that you
06:04	started from . Okay , now that you know what
06:07	degrees are and you've seen how they relate to the
06:09	size of an angle . We need to learn how
06:11	to actually measure an angle . Without this fancy readout
06:14	that we have here , just like a ruler can
06:16	be used to measure the length of a line .
06:18	A special tool called a protractor can be used to
06:21	measure angles . A protractor is similar to a ruler
06:25	but it's curved into a half circle so that it
06:28	can measure rotation around an axis point . A protractor
06:31	also has a straight edge with a hole or a
06:33	dot in the middle that represents the axis or centre
06:36	of rotation . So if you're given a mystery angle
06:39	like this one and you want to measure how many
06:41	degrees it is , you just put your protractor on
06:44	top of it so that the access point lines up
06:46	with the intersection of your race like this . Then
06:49	you make sure that one of the rays lines up
06:51	with the straight line on the protractor . And last
06:54	of all , you look to see where the other
06:55	ray crosses the curved part and read off what angle
06:58	measurement it lines up with . As you can see
07:01	this angle here is 50°. . All right . There's
07:05	one more thing I want to teach you in this
07:06	video because you'll probably see this kind of geometry problem
07:09	on your homework or tests . Do you remember what
07:12	complementary and supplementary angles are from the last video ,
07:15	Complementary angles combined to form a right angle and supplementary
07:19	angles combined to form a straight angle . Well ,
07:22	now that we know that a right angle is 90°
07:25	and a straight angle is 180°, , we can use
07:28	that information to solve problems that have unknown angles like
07:31	this one . It shows two angles , angle and
07:34	angle be that combined to form a right angle .
07:37	The problem tells us that angle a is 30° and
07:41	it wants us to figure out what angle B is
07:44	. Fortunately it's easy to figure that out now because
07:47	we know that a right angle is 90°. . So
07:49	we know what the total of both angles must be
07:53	. That means that defined angle be . All we
07:55	have to do is take the total which is 90°
07:58	and subtract angle a which is 30° and whatever's left
08:01	over will be the measurement of angle be So 90
08:06	-30 equals 60 . So angle B is 60°. .
08:10	Now let's try this problem . It uses the same
08:13	idea , but with the straight angle this time the
08:16	straight angle is divided into two smaller angles . Again
08:19	, angle and angle be And again the problem tells
08:22	us that angle a is 70° and it wants us
08:25	to figure out what angle B is . Well ,
08:29	we know that the total of both angles must be
08:31	180° because we just learned that that's how big a
08:34	straight angle is . So if we take that total
08:37	180 degrees and subtract angle A . Which is 70
08:40	degrees . Whatever is left over after subtracting must be
08:44	and will be so 1 80 minus 70 equals 110
08:50	. Pretty cool . Huh ? And now you can
08:52	see why it's important to know how degrees work in
08:54	geometry . Uh They can tell us how big angles
08:57	are or how much something is rotated . Well that's
09:00	all I've got for you in this video . But
09:02	don't worry , there's a lot more geometry where that
09:04	came from . So I'll get going on my next
09:06	video and you get going on practicing what you've learned
09:09	. Thanks for watching mathematics . And I'll see you
09:11	next time . Learn more at math Antics dot com
00:0-1	.

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