0:00:00.950,0:00:03.460
So let's review everything that[br]we know so far, because it's

0:00:03.460,0:00:05.470
good to keep reviewing.

0:00:05.470,0:00:07.360
Because these are things[br]you should never forget

0:00:07.360,0:00:08.870
the rest of your life.

0:00:08.870,0:00:14.330
So if I have a line and if I[br]draw an angle that goes--

0:00:14.330,0:00:16.530
let's say this is the[br]pivot point, right?

0:00:16.530,0:00:19.790
If I go all the way around[br]the line, or in a circle,

0:00:19.790,0:00:20.975
that's 360 degrees.

0:00:20.975,0:00:23.970
[br]11[br]00:00:23,97 --> 00:00:27,43[br]We learned that there are[br]360 degrees in a circle.

0:00:27.430,0:00:28.750
Right?

0:00:28.750,0:00:32.440
We also learned that if[br]I have lines like this.

0:00:32.440,0:00:41.140
If I have two angles-- let[br]me draw it like that.

0:00:41.140,0:00:43.710
[br]16[br]00:00:43,71 --> 00:00:49,49[br]And this is angle x.

0:00:49.490,0:00:50.625
This is angle y.

0:00:50.625,0:00:54.122
[br]19[br]00:00:54,122 --> 00:00:57,825[br]x and y are supplementary.

0:00:57.825,0:01:04.240
[br]21[br]00:01:04,24 --> 00:01:07,63[br]And that just means that[br]they add up to 180 degrees.

0:01:07.630,0:01:10.810
x plus y is equal[br]to 180 degrees.

0:01:10.810,0:01:11.920
And why does that make sense?

0:01:11.920,0:01:16.200
Because look, if we add[br]up x plus y we have gone

0:01:16.200,0:01:19.450
halfway around the circle.

0:01:19.450,0:01:22.040
So that's 180 degrees, right?

0:01:28.620,0:01:31.380
So hopefully we[br]have learned that.

0:01:31.380,0:01:35.316
And then let me switch colors[br]for the sake of variety.

0:01:35.316,0:01:39.080
Let me use my line tool.

0:01:39.080,0:01:44.140
If I have-- let's see,[br]I'm going to draw

0:01:44.140,0:01:46.050
perpendicular lines.

0:01:46.050,0:01:50.220
If I have that line, and[br]then I have that line.

0:01:50.220,0:01:52.080
And they are perpendicular.

0:01:52.080,0:01:55.270
And then I have another line.

0:01:55.270,0:01:56.870
Let's say it goes like that.

0:01:56.870,0:01:59.830
[br]39[br]00:01:59,83 --> 00:02:03,73[br]And then I say that[br]this is angle x.

0:02:03.730,0:02:05.030
Woops.

0:02:05.030,0:02:07.650
This is angle x.

0:02:07.650,0:02:09.240
And this is angle y.

0:02:09.240,0:02:12.290
[br]44[br]00:02:12,29 --> 00:02:16,04[br]Well, I said this line and this[br]line are perpendicular, right?

0:02:16.040,0:02:18.390
So that means that they[br]intersect at a 90 degree angle.

0:02:18.390,0:02:20.710
So we know that this whole[br]thing is 90 degrees.

0:02:20.710,0:02:24.070
[br]48[br]00:02:24,07 --> 00:02:26,01[br]And so what do we[br]know about x plus y?

0:02:26.010,0:02:29.435
Well, x plus y is going[br]to equal 90 degrees.

0:02:29.435,0:02:34.130
[br]51[br]00:02:34,13 --> 00:02:41,33[br]Or we could say that x[br]and y are complementary.

0:02:41.330,0:02:43.920
And I always get confused[br]between supplementary

0:02:43.920,0:02:44.670
and complementary.

0:02:44.670,0:02:45.910
You just got to memorize it.

0:02:45.910,0:02:47.470
I don't know if there's[br]any-- let's see, is

0:02:47.470,0:02:48.650
there any easy way?

0:02:48.650,0:02:51.950
180, supplementary.

0:02:51.950,0:02:56.890
You could say that 180-- 100[br]starts with an O, which

0:02:56.890,0:02:58.950
supplementary does[br]not start with.

0:02:58.950,0:03:00.080
So there.

0:03:00.080,0:03:01.500
There's your mnemonic.

0:03:01.500,0:03:02.910
Complementary.

0:03:02.910,0:03:05.100
And 90 starts with an N,[br]and complementary does

0:03:05.100,0:03:05.920
not start with an N.

0:03:05.920,0:03:07.450
That's your other mnemonic.

0:03:07.450,0:03:07.930
Complementary.

0:03:07.930,0:03:15.420
[br]68[br]00:03:15,42 --> 00:03:16,59[br]I don't know if I'm[br]spelling it right.

0:03:16.590,0:03:17.590
Who cares?

0:03:17.590,0:03:18.750
Let's move on.

0:03:18.750,0:03:20.190
So let's learn some more[br]stuff about angles.

0:03:20.190,0:03:22.490
And what I'm going to do is I'm[br]going to give you an arsenal,

0:03:22.490,0:03:25.640
and then once you have that[br]arsenal you can just tackle

0:03:25.640,0:03:28.280
these beastly problems that[br]I'm going to throw at you.

0:03:28.280,0:03:31.960
So just take these for granted[br]right now, and then in a few

0:03:31.960,0:03:34.630
videos, probably, we're[br]going to tackle some

0:03:34.630,0:03:35.505
beastly problems.

0:03:35.505,0:03:38.220
[br]79[br]00:03:38,22 --> 00:03:40,48[br]And you know, I'm[br]using variables here.

0:03:40.480,0:03:41.486
And if you're not familiar[br]with variables you

0:03:41.486,0:03:42.135
can put numbers here.

0:03:42.135,0:03:46.050
If x was 30 degrees, then y[br]is going to be 60 degrees.

0:03:46.050,0:03:46.670
Right?

0:03:46.670,0:03:51.050
Or in this case, if x is, I[br]don't know, 45 degrees, then y

0:03:51.050,0:03:53.960
is going to be 135 degrees.

0:03:53.960,0:03:54.560
That other way.

0:03:54.560,0:03:59.290
Let me draw another property of[br]angles of intersecting lines.

0:03:59.290,0:04:05.890
So if I have two angles, two[br]lines that intersect like this.

0:04:05.890,0:04:08.560
[br]90[br]00:04:08,56 --> 00:04:10,76[br]So a couple of[br]interesting things.

0:04:10.760,0:04:14.695
So first, I'm going to teach[br]you about opposite angles.

0:04:14.695,0:04:17.490
[br]93[br]00:04:17,49 --> 00:04:19,51[br]Let me switch colors.

0:04:19.510,0:04:22.860
Let me switch to yellow.

0:04:22.860,0:04:30.710
So if this is x degrees, then[br]it turns out that the angle

0:04:30.710,0:04:34.110
opposite to it is also[br]equal to x degrees.

0:04:34.110,0:04:40.430
[br]98[br]00:04:40,43 --> 00:04:42,18[br]And you don't believe me?

0:04:42.180,0:04:44.550
Well let me prove it to you.

0:04:44.550,0:04:49.900
Let's say we call this,[br]I don't know, let's

0:04:49.900,0:04:52.800
call this y degrees.

0:04:52.800,0:04:53.560
Right?

0:04:53.560,0:04:55.520
And I'm going to prove[br]to you that the x and

0:04:55.520,0:04:57.020
the y are the same.

0:04:57.020,0:04:58.680
Well what do we know already?

0:04:58.680,0:05:01.640
Let's call this other angle--[br]and I'm doing this to

0:05:01.640,0:05:10.530
confuse you-- angle z.

0:05:10.530,0:05:14.940
Well what do we know about[br]angle x and angle z?

0:05:14.940,0:05:17.160
It may not be obvious to you[br]because I've drawn it slightly

0:05:17.160,0:05:21.350
different, but I'll give you[br]a small hint with

0:05:21.350,0:05:26.310
an appropriately[br]interesting color.

0:05:26.310,0:05:31.870
So what angle is this[br]whole thing right here?

0:05:31.870,0:05:33.550
Well I'm just going[br]along a line, right?

0:05:33.550,0:05:35.600
That's halfway around a circle.

0:05:39.190,0:05:41.250
So what does x plus z equal?

0:05:41.250,0:05:44.820
Well, x plus z is going to[br]equal that larger angle.

0:05:44.820,0:05:54.040
x plus purple z is going to[br]equal-- I think I'll switch to

0:05:54.040,0:05:57.030
the blue; maybe it's taking too[br]much time for me to switch--

0:05:57.030,0:05:58.890
is equal to 180 degrees.

0:05:58.890,0:06:03.580
Or x and z are supplementary.

0:06:03.580,0:06:09.240
[br]124[br]00:06:09,24 --> 00:06:10,63[br]I've run out of space.

0:06:10.630,0:06:12.900
So what do we know about z?

0:06:12.900,0:06:20.400
Well z is equal to 180 minus x.

0:06:20.400,0:06:20.750
Right?

0:06:20.750,0:06:23.070
Because x plus z is 180.

0:06:23.070,0:06:24.540
Fine.

0:06:24.540,0:06:27.850
Now, what's the relationship[br]between z and y?

0:06:27.850,0:06:31.770
Well, z and y are[br]also supplementary.

0:06:31.770,0:06:37.210
Because look, if I[br]drew this angle here.

0:06:37.210,0:06:38.792
Look at this big angle.

0:06:38.792,0:06:42.070
[br]135[br]00:06:42,07 --> 00:06:42,69[br]What angle is that?

0:06:42.690,0:06:45.260
Well once again I'm still going[br]halfway around the circle.

0:06:45.260,0:06:45.990
Right?

0:06:45.990,0:06:48.390
But now I'm using this[br]line right here.

0:06:48.390,0:06:51.230
So that's 180 degrees.

0:06:51.230,0:06:56.440
So we know that angle z[br]plus angle y is also

0:06:56.440,0:06:57.685
equal to 180 degrees.

0:06:57.685,0:07:05.540
[br]143[br]00:07:05,54 --> 00:07:06,82[br]Right?

0:07:06.820,0:07:08.930
Or, I don't want to keep[br]writing it, but z and y

0:07:08.930,0:07:11.670
are also supplementary.

0:07:11.670,0:07:14.500
But we just figured out[br]that z is 180 minus x.

0:07:14.500,0:07:15.140
Right?

0:07:15.140,0:07:18.960
So let's just substitute[br]that back in here.

0:07:18.960,0:07:29.420
So we get 180 minus x plus[br]y is equal to 180 degrees.

0:07:29.420,0:07:31.690
Why don't we subtract 180[br]degrees from both sides

0:07:31.690,0:07:32.960
of this equation.

0:07:32.960,0:07:39.540
That cancels out, and we get[br]minus x plus y is equal to 0.

0:07:39.540,0:07:41.730
And then add x to both sides[br]of this equation, and

0:07:41.730,0:07:46.030
we get y is equal to x.

0:07:52.080,0:07:54.950
So x is equal to y.

0:07:54.950,0:07:56.730
And if you've played around[br]with this, if you just drew a

0:07:56.730,0:07:59.160
bunch of straight lines and[br]they intersected at different

0:07:59.160,0:08:02.720
angles, I think when you[br]eyeball it it would make sense.

0:08:02.720,0:08:06.590
And then similarly, if that's z[br]then the other opposite angle

0:08:06.590,0:08:15.510
here is also z degrees.

0:08:15.510,0:08:16.790
So what do we know now?

0:08:16.790,0:08:20.870
The total angles in a[br]circle, 360 degrees.

0:08:20.870,0:08:24.380
When two angles kind of[br]combine, go halfway around the

0:08:24.380,0:08:28.520
circle-- or they combine,[br]kind of form a line.

0:08:28.520,0:08:30.530
There's different ways[br]you can think about it.

0:08:30.530,0:08:31.370
We know they're supplementary.

0:08:31.370,0:08:33.350
They add up to 180 degrees.

0:08:33.350,0:08:34.920
x plus y is 180 degrees.

0:08:34.920,0:08:38.360
If they add up to 90[br]it's complementary.

0:08:38.360,0:08:39.570
x plus y is 90.

0:08:39.570,0:08:42.020
And then opposite angles[br]are equal to each other.

0:08:42.020,0:08:42.350
Right?

0:08:42.350,0:08:46.130
This angle is equal[br]to this angle.

0:08:46.130,0:08:49.310
And then this angle is going to[br]be equal to this angle for the

0:08:49.310,0:08:50.990
same reason-- because[br]it's opposite.

0:08:50.990,0:08:54.355
In the next video I'm going[br]to show you about parallel

0:08:54.355,0:08:55.940
lines and transversals.

0:08:55.940,0:08:59.170
More fancy words for what[br]I think are fairly

0:08:59.170,0:09:00.520
straightforward concepts.

0:09:00.520,0:09:03.796
I'll see you in the next video.