WEBVTT
1
00:00:00.000 --> 00:00:04.000
Hi, this is Julie Harland and I'm your math gal.
2
00:00:04.000 --> 00:00:14.000
Please visit my website at yourmathgal.com where you could search for any of my videos organized by topic.
3
00:00:14.000 --> 00:00:17.000
This is part one of angles. It's an introduction.
4
00:00:17.000 --> 00:00:24.000
And on this video we define several terms associated with angles and we do four problems
5
00:00:24.000 --> 00:00:29.000
finding the complement or supplement of a given angle.
6
00:00:29.000 --> 00:00:34.000
We're going to start out with some basics about angles in general.
7
00:00:34.000 --> 00:00:39.000
So a unit used to measure angles is the degree.
8
00:00:39.000 --> 00:00:44.000
And the symbol for degree is this little circle here as in 30 degrees.
9
00:00:44.000 --> 00:00:51.000
And this symbol here kind of looks like a less than symbol is the symbol used for angle.
10
00:00:51.000 --> 00:00:55.000
Now if you have, let's say, line right here,
11
00:00:55.000 --> 00:01:01.000
and I want to do a full revolution so I'm going to like go around all the way around here.
12
00:01:01.000 --> 00:01:09.000
When full revolution, which could be considered an angle, is actually 360 degrees.
13
00:01:09.000 --> 00:01:16.000
So one full revolution is 360 degrees.
14
00:01:16.000 --> 00:01:19.000
Now we could have angle of all sizes.
15
00:01:19.000 --> 00:01:26.000
We have what's called an acute angle.
16
00:01:26.000 --> 00:01:33.000
That would be it's less than 90 degrees.
17
00:01:33.000 --> 00:01:47.000
And an ob-2 single is between 90 degrees and 180 degrees.
18
00:01:47.000 --> 00:01:54.000
So knowing this it might be useful to think about where 90 degrees and where 180 degrees is.
19
00:01:54.000 --> 00:01:57.000
So let's see.
20
00:01:57.000 --> 00:02:00.000
I just think of this plane here.
21
00:02:00.000 --> 00:02:06.000
If I go up all the way around it's 360 degrees, then if I only go that far around,
22
00:02:06.000 --> 00:02:08.000
that should be 180 degrees.
23
00:02:08.000 --> 00:02:12.000
So I could say this is a 180 degree angle right there.
24
00:02:12.000 --> 00:02:17.000
So 180 degree angle actually forms a straight line.
25
00:02:17.000 --> 00:02:27.000
So we say 180 degree angle is called a straight angle.
26
00:02:27.000 --> 00:02:36.000
Now what about 90 degrees?
27
00:02:36.000 --> 00:02:38.000
Well that would only be halfway up.
28
00:02:38.000 --> 00:02:45.000
So if I want to look at the 90 degree angle, it would be up through here.
29
00:02:45.000 --> 00:02:49.000
That would be 90 degrees.
30
00:02:49.000 --> 00:03:02.000
So we say 90 degrees is called a right angle.
31
00:03:02.000 --> 00:03:09.000
And a symbol we use for a right angle looks like this.
32
00:03:09.000 --> 00:03:12.000
Okay, it's kind of squared off because you could think of this right here.
33
00:03:12.000 --> 00:03:15.000
It's squared off, these are perpendicular lines.
34
00:03:15.000 --> 00:03:19.000
So that would be a right angle, 90 degrees.
35
00:03:19.000 --> 00:03:22.000
So looking back up, we've got going all the way around.
36
00:03:22.000 --> 00:03:25.000
One full revelation is 360 degrees.
37
00:03:25.000 --> 00:03:29.000
Half way around, we get a straight angle, 180 degrees.
38
00:03:29.000 --> 00:03:32.000
Going a quarter the way around, that's a right angle.
39
00:03:32.000 --> 00:03:34.000
And that would be 90 degrees.
40
00:03:34.000 --> 00:03:38.000
And then we also talked about an acute angle, less than 90 degrees.
41
00:03:38.000 --> 00:03:40.000
So it's somewhere smaller than this.
42
00:03:40.000 --> 00:03:41.000
It's a smaller angle.
43
00:03:41.000 --> 00:03:44.000
So what would a picture of an acute angle be?
44
00:03:44.000 --> 00:03:47.000
It might look something like this.
45
00:03:47.000 --> 00:03:50.000
All right, kind of small.
46
00:03:50.000 --> 00:03:52.000
And what would an obtuse angle be?
47
00:03:52.000 --> 00:03:56.000
It would be bigger than this 90 degree, but not all the way over to here.
48
00:03:56.000 --> 00:04:03.000
So an obtuse angle might look, let's see, let's do this again.
49
00:04:03.000 --> 00:04:07.000
Might look something like this.
50
00:04:07.000 --> 00:04:13.000
That would be an obtuse angle, right, in between 90 and 180 degrees.
51
00:04:13.000 --> 00:04:18.000
So there's a lot of definition here, but you get used to it fairly quickly.
52
00:04:18.000 --> 00:04:24.000
Acute, less than 90 obtuse, bigger than 90, but still less than 180.
53
00:04:24.000 --> 00:04:33.000
And then we have the 90, 180, and 360, the right angle, the straight angle, and the full revelation.
54
00:04:33.000 --> 00:04:38.000
We just have a couple more words we're going to learn right now.
55
00:04:38.000 --> 00:04:41.000
Complimentary and supplementary angles.
56
00:04:41.000 --> 00:04:46.000
And they have to do with a 90 or the 180 degree angle.
57
00:04:46.000 --> 00:04:49.000
All right, first let's define complementary angles.
58
00:04:49.000 --> 00:04:55.000
Complementary angles are two angles that add up to 90 degrees.
59
00:04:55.000 --> 00:04:56.000
So here's some examples.
60
00:04:56.000 --> 00:05:00.000
You think of two numbers that add up to 90 degrees.
61
00:05:00.000 --> 00:05:13.000
So 30 degrees and 60 degrees are complementary angles.
62
00:05:13.000 --> 00:05:16.000
Okay, what would be another example?
63
00:05:16.000 --> 00:05:19.000
What would it be if I had 10 degrees?
64
00:05:19.000 --> 00:05:21.000
What would the other angle be?
65
00:05:21.000 --> 00:05:28.000
Now keep in mind the other angle when added to 10 degrees has to add up to 90, so what would that be?
66
00:05:28.000 --> 00:05:30.000
Well, that would have to be 80 degrees.
67
00:05:30.000 --> 00:05:39.000
And you can get that by the 90 minus 10, for instance, 10 degrees and 80 degrees are also complementary angles.
68
00:05:39.000 --> 00:05:46.000
So there's just two angles that add up to 90 degrees.
69
00:05:46.000 --> 00:05:48.000
Next we have supplementary angles.
70
00:05:48.000 --> 00:05:53.000
Supplementary angles are two angles that add up to 180 degrees.
71
00:05:53.000 --> 00:05:59.000
Okay, the way I remember these when I first learned them is in the alphabet C becomes before S.
72
00:05:59.000 --> 00:06:05.000
So that's the 90 degree, and the supplementary would be the 180 degrees.
73
00:06:05.000 --> 00:06:07.000
Okay, whatever works for you.
74
00:06:07.000 --> 00:06:15.000
So what are some examples of supplementary angles?
75
00:06:15.000 --> 00:06:18.000
There's my abbreviation.
76
00:06:18.000 --> 00:06:21.000
Even though it's kind of funny to use it in a positive way.
77
00:06:21.000 --> 00:06:22.000
Right?
78
00:06:22.000 --> 00:06:27.000
How about if I had 40 degrees and what would the other be?
79
00:06:27.000 --> 00:06:34.000
Okay, two angles have to add up to 180 degrees, so if one's 40, what would the other one be?
80
00:06:34.000 --> 00:06:38.000
140 degrees.
81
00:06:38.000 --> 00:06:40.000
Another possibility?
82
00:06:40.000 --> 00:06:46.000
How about 100 degrees and what would the other one be?
83
00:06:46.000 --> 00:06:47.000
80 degrees.
84
00:06:47.000 --> 00:06:52.000
Now, what if I said, you know, 56 degrees?
85
00:06:52.000 --> 00:06:56.000
You might not be able to do that in your head, but could you figure it out?
86
00:06:56.000 --> 00:06:59.000
Any ideas how do you figure out what the other one is?
87
00:06:59.000 --> 00:07:06.000
I would just subtract the 56 from 180.
88
00:07:06.000 --> 00:07:07.000
And see what you get.
89
00:07:07.000 --> 00:07:13.000
I think that's 124.
90
00:07:13.000 --> 00:07:17.000
And you could verify that is 56 plus 124.
91
00:07:17.000 --> 00:07:19.000
Does that add up to 180?
92
00:07:19.000 --> 00:07:21.000
And if so, then that would be correct.
93
00:07:21.000 --> 00:07:26.000
So those are examples of supplementary degrees.
94
00:07:26.000 --> 00:07:29.000
Okay, it's time for you to try a few problems on your own.
95
00:07:29.000 --> 00:07:33.000
So put the video on pause and try these four problems.
96
00:07:33.000 --> 00:07:35.000
All right, let's do number one.
97
00:07:35.000 --> 00:07:38.000
Find the complement of a 15 degree angle.
98
00:07:38.000 --> 00:07:40.000
So remember, the complement.
99
00:07:40.000 --> 00:07:44.000
Well, complementary angles are two angles that add up to 90 degrees.
100
00:07:44.000 --> 00:07:51.000
So we have to think of what the other angle is that we could add to 15 to get 90.
101
00:07:51.000 --> 00:07:54.000
Now, you could use algebra to do this by thinking, well,
102
00:07:54.000 --> 00:07:57.000
the number I'm looking for, I'm going to call it C,
103
00:07:57.000 --> 00:08:01.000
and I know when I add it to 15, I would get 90.
104
00:08:01.000 --> 00:08:04.000
So you could like make an equation up to figure this out.
105
00:08:04.000 --> 00:08:10.000
Or some of you probably could figure that out in your head that it would be 75.
106
00:08:10.000 --> 00:08:15.000
But if you wrote it as an equation, we could write C plus 15 is 90.
107
00:08:15.000 --> 00:08:19.000
And when you subtract 15 from both sides, you'll get 75.
108
00:08:19.000 --> 00:08:21.000
But of course, this is an equation you made up.
109
00:08:21.000 --> 00:08:24.000
We're not just solving equation, what's the complement?
110
00:08:24.000 --> 00:08:30.000
Our answer will be in degrees, 75 degrees.
111
00:08:30.000 --> 00:08:35.000
So not necessary to write an equation, but it's certainly okay to do it.
112
00:08:35.000 --> 00:08:40.000
And some people may just figure what they have to add to 15 to get 90.
113
00:08:40.000 --> 00:08:45.000
Some may actually get out a piece of paper and do 90 minus 15 to get 75.
114
00:08:45.000 --> 00:08:48.000
And some people will write an equation and solve the equation.
115
00:08:48.000 --> 00:08:51.000
Either way is fine. Any of those ways.
116
00:08:51.000 --> 00:08:56.000
Have one number two. Find the supplement of a 15-degree angle.
117
00:08:56.000 --> 00:09:02.000
Alright, so now we want to find an angle that's a supplement of 15.
118
00:09:02.000 --> 00:09:08.000
So again, if you want to try an equation, you can, let's say I call it X,
119
00:09:08.000 --> 00:09:13.000
when I add 15, I would get 180 degrees.
120
00:09:13.000 --> 00:09:17.000
Actually, I'm just going to write 180 and not worry about the degree angle.
121
00:09:17.000 --> 00:09:22.000
Not worry about the degrees till later.
122
00:09:22.000 --> 00:09:25.000
So what would that be?
123
00:09:25.000 --> 00:09:29.000
By subtract 15, it'd be 165.
124
00:09:29.000 --> 00:09:33.000
And so we'd have 165 degrees.
125
00:09:33.000 --> 00:09:34.000
That would be the supplement.
126
00:09:34.000 --> 00:09:37.000
Now you can always check your answer by adding the two angles.
127
00:09:37.000 --> 00:09:41.000
Is 15 plus 7590? That would be the answer for number one.
128
00:09:41.000 --> 00:09:47.000
And is 165 plus 15 equal to 180.
129
00:09:47.000 --> 00:09:49.000
Yes, then there's supplementary angles.
130
00:09:49.000 --> 00:09:54.000
Alright, number three. Find the complement of a 71-degree angle.
131
00:09:54.000 --> 00:10:02.000
Again, up to you if you want to write an equation, we could call it C plus 71 equals 90.
132
00:10:02.000 --> 00:10:08.000
And when you subtract 71, you get 19.
133
00:10:08.000 --> 00:10:11.000
So my answer here would be 19 degrees.
134
00:10:11.000 --> 00:10:17.000
And again, you would verify that 71 plus 19 equals 90.
135
00:10:17.000 --> 00:10:21.000
And the last one, find the supplement of 120-degree angle.
136
00:10:21.000 --> 00:10:23.000
This one's pretty easy to do in your head.
137
00:10:23.000 --> 00:10:26.000
What do you add to 120 to get to 180?
138
00:10:26.000 --> 00:10:30.000
That would just be 60 degrees.
139
00:10:30.000 --> 00:10:36.000
So remember, using equations can be helpful
140
00:10:36.000 --> 00:10:38.000
to find the answer to a problem.
141
00:10:38.000 --> 00:10:40.000
This isn't asking you to write an equation.
142
00:10:40.000 --> 00:10:43.000
It just asks you to find the complement or the supplement of any angle.
143
00:10:43.000 --> 00:10:48.000
And so however you figure it out would be fine, but you could write an equation.
144
00:10:48.000 --> 00:10:50.000
That's what's cool about algebra.
145
00:10:50.000 --> 00:10:55.000
Sometimes equations make it easier for some people to find the answer.
146
00:10:55.000 --> 00:11:00.000
On the next video, angles two will do more problems.
147
00:11:00.000 --> 00:11:03.000
We're using algebra to find the answer will be useful.
148
00:11:03.000 --> 00:11:10.000
And you probably will need to use algebra in many of these cases.
149
00:11:10.000 --> 00:11:22.000
Please visit my website at yourmathgal.com where you can view all of my videos,
150
00:11:22.000 --> 00:11:26.000
which are organized by topic.