0:00:00.930,0:00:03.630
Let's play the angle game.

0:00:03.630,0:00:07.170
So I've drawn this crazy figure[br]here and I'm going to give you

0:00:07.170,0:00:09.590
a couple of angles and then I[br]want you to figure

0:00:09.590,0:00:10.950
out another angle.

0:00:10.950,0:00:13.350
So let me give you some angles.

0:00:13.350,0:00:24.970
So let's say that this angle[br]up here is 56 degrees.

0:00:28.755,0:00:38.108
Then I also tell you this angle here is 115 degrees.

0:00:41.862,0:00:46.016
What I would like you to figure out -- this is the object of

0:00:46.016,0:00:50.040
the angle game -- I want you to[br]figure out what this

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angle is - right here.

0:00:55.360,0:00:59.313
If you are brave, you can pause the video and try to

0:00:59.313,0:01:00.997
figure it out yourself.

0:01:00.997,0:01:02.815
If you would like me to walk[br]you through it -- and maybe I

0:01:02.815,0:01:04.520
can give you a couple of steps[br]and then you pause it and you

0:01:04.520,0:01:05.970
get the rest of it by yourself.

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But I will now show you[br]how I would have solved

0:01:08.410,0:01:10.810
this in the angle game.

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You have all the tools[br]necessary to already solve it.

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I want you to be able to get[br]good at this, because this is

0:01:16.420,0:01:19.800
kind of like the key[br]skill on the SAT.

0:01:19.800,0:01:22.080
Oh, I didn't give you a key[br]piece of -- you're probably

0:01:22.080,0:01:23.560
saying I can't solve this.

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You probably can't because[br]I haven't given you a key

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piece of information.

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This line here and this line[br]here, so this line and this

0:01:29.510,0:01:32.130
line, they're parallel.

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I was telling you to solve[br]it before giving you a

0:01:34.330,0:01:35.290
key piece of information.

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That means that[br]they are parallel.

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So what can we do this figure?

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So whenever I see these type of[br]problems, either while playing

0:01:41.500,0:01:46.890
the angle game or on, say, an[br]SAT, I just literally kind of

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figure out every angle that I[br]can figure out and slowly try

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to make my way to[br]the goal angle.

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Let's see what we can[br]figure out here.

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So I'm going to do it in this[br]blue-green color anything

0:01:58.080,0:02:00.070
that I can figure out.

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So this angle is 56[br]degrees, right?

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These lines are parallel.

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This line here looks like a transversal -- a transversal!

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So what do we know about it?

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Well, let's see, what's a corresponding angle to

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this angle right here?

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Well, it's the angle, right?

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What do we know about[br]corresponding angles for

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parallel lines when you have a transversal?

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That's 56 degrees.

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56 degrees - right? Because corresponding angles are equal.

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We could have done a[br]lot of other stuff.

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We could have figured out that[br]this angle is 56 degrees, but

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that probably wouldn't have[br]gotten us closer to our goal.

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That angle's 56 degrees and[br]its corresponding angle

0:02:40.150,0:02:41.580
is also 56 degrees.

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That wouldn't have gotten[br]us any closer to our goal.

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We could have figured out that[br]this is 180 minus 56, right,

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which is, what? 124 degrees.

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That really wouldn't[br]have helped us much.

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I'm showing you, these are all[br]things that you can do while

0:02:53.540,0:02:54.870
playing the angle game.

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But anyway, the first step[br]-- I said well, these are

0:02:57.380,0:03:00.810
corresponding angles,[br]so that's 56 degrees.

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So let's see, I need to figure[br]out this angle right here.

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I know this one, and they're[br]in a triangle, right?

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You see this triangle.

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If only I knew this angle.

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Can you figure out this angle?

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Well, it is supplementary to[br]this 115 degrees, right?

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So this green angle plus this purple angle

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is equal to 180. So this is 180 minus 115.

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So what's that? 180 minus -- so this[br]is 65 degrees.

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So what have we done so far?

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We just said well these[br]are parallel lines, so

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corresponding angles are equal.

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So this 56 degrees is[br]equal to this 56 degrees.

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Then we said, well, this green[br]angle and this purple angle are

0:03:47.240,0:03:49.110
supplementary, so they[br]have to add up to 180.

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So this is 115.

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But this is 65, which[br]is just 180 minus 115.

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I think you might see[br]where I'm going now.

0:03:57.690,0:04:02.640
Now we know two angles[br]of a triangle.

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If we know two angles of a[br]triangle, what can figure

0:04:05.440,0:04:05.960
out about the third?

0:04:05.960,0:04:09.870
Well, we know the angles of a[br]triangle add up to 180, right?

0:04:09.870,0:04:13.210
So let's called this x.

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We know that x plus 56[br]plus 65 equals 180.

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What's 56 plus 65?

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This is where I always[br]mess up, on the addition

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and the subtraction.

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So, 5 plus 6 is 110.

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This is 121 I believe.

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121, right? ... right, 121 equals 180.

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Then x is equal to --[br]let's see, 180 minus

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20 is 60, so it's 59.

0:04:46.040,0:04:49.462
x is equal to 59 degrees.

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There we go.

0:04:53.701,0:04:59.215
We have accomplished our first[br]goal in the angle game.

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There you saw it.

0:05:00.321,0:05:03.005
So let's do a tougher[br]angle problem.

0:05:06.390,0:05:09.536
This one maybe won't involve parallel lines.

0:05:09.536,0:05:11.400
But I just want to show you,[br]everything really just boils

0:05:11.400,0:05:15.280
down to everything we learned[br]about parallel lines and

0:05:15.280,0:05:18.340
triangles and angles[br]adding up to each other.

0:05:18.340,0:05:20.811
So this one involves a star.

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Let me draw the star.

0:05:24.730,0:05:27.959
So, let's see -- a line from there to there.

0:05:27.959,0:05:30.405
Draw a line from there to there.

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Draw a line from there to there.

0:05:33.624,0:05:36.515
Draw a line from there to there.

0:05:37.192,0:05:39.840
Draw a line from there to there.

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What do we know about this?

0:05:41.510,0:05:44.400
We know that this angle[br]is 75 -- oh boy, I'm

0:05:44.400,0:05:45.410
using the wrong tool.

0:05:45.410,0:05:48.750
This angle is 75 degrees.

0:05:48.750,0:05:54.280
We also know that this[br]angle is 75 degrees.

0:05:54.280,0:06:00.300
We know this angle[br]here is 101 degrees.

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Your mission in this angle[br]game is to figure out

0:06:06.640,0:06:08.920
this angle right here.

0:06:08.920,0:06:10.910
What is this angle?

0:06:10.910,0:06:13.030
This is a good time to[br]pause because I will now

0:06:13.030,0:06:14.550
show you the solution.

0:06:14.550,0:06:15.560
So what can we do here?

0:06:15.560,0:06:19.230
So this angle, well jeez, I[br]just like to just mess around

0:06:19.230,0:06:20.690
and see what I can figure out.

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So, if this angle here is[br]101 degrees, what other

0:06:23.800,0:06:24.880
angles can we figure out?

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We could figure out -- well, we[br]could figure out this angle.

0:06:27.550,0:06:28.540
We could figure out[br]a bunch of angles.

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We could figure out that -- let[br]me switch the color, these

0:06:31.640,0:06:33.720
are my "figure out" angles.

0:06:33.720,0:06:37.010
So that's 101, then this[br]is supplementary, that's

0:06:37.010,0:06:39.110
79 degrees, right?

0:06:39.110,0:06:44.190
That's also 79 degrees because[br]this is also supplementary.

0:06:44.190,0:06:46.100
This angle right here is[br]opposite to it, so this

0:06:46.100,0:06:49.487
angle right here is[br]going to be 101 degrees.

0:06:51.948,0:06:54.372
What else can figure out?

0:06:54.372,0:06:56.510
We could figure out this angle[br]because it's supplementary, we

0:06:56.510,0:06:57.910
could figure out this angle.

0:06:57.910,0:06:59.700
We could also figure out this[br]angle because we see this

0:06:59.700,0:07:01.380
triangle right here.

0:07:01.380,0:07:07.860
This angle plus 75 plus 75 is[br]going to equal 180, right?

0:07:07.860,0:07:12.180
So let's call this[br]angle b, b for blue.

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So b plus 75 plus 75 is[br]going to equal 180.

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And I'm just using this[br]triangle right here.

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So b plus 150 is equal to 180,[br]or b is equal to 30 degrees.

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So we're able to[br]figure this out.

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Now, what will you do if I told you that

0:07:38.366,0:07:41.280
we are now ready to figure out this yellow angle?

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It might not be obvious to you.

0:07:42.260,0:07:43.965
You kind of have to look at the[br]triangle in the right way, and

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the SAT will do this to you[br]all the time, all the time.

0:07:46.850,0:07:49.170
That's why I'm testing[br]you this way.

0:07:49.170,0:07:51.740
Well, let me give you a little hint:

0:07:51.740,0:07:53.740
Look at this triangle.

0:07:55.647,0:07:59.717
Non-ideal color, let me do it in red so it really stands out.

0:08:00.360,0:08:02.590
Look at this triangle.

0:08:02.590,0:08:04.290
I'll tell you, the hardest[br]thing about these problems is

0:08:04.290,0:08:07.140
just looking at the right[br]triangle and kind of seeing

0:08:07.140,0:08:11.260
that oh wow, I actually[br]can figure out something.

0:08:11.260,0:08:14.800
Look at this triangle[br]right here.

0:08:14.800,0:08:17.380
We know this angle[br]of it, 101 degrees.

0:08:17.380,0:08:19.040
We know this angle, we[br]just figured it out,

0:08:19.040,0:08:20.970
it was 30 degrees.

0:08:20.970,0:08:23.210
So all we have left is to[br]figure out this yellow

0:08:23.210,0:08:25.313
angle, call it x.

0:08:28.805,0:08:35.490
So x plus 101 ... plus 30 is equal to 180 degrees because

0:08:35.490,0:08:38.430
the angles in a triangle[br]add up to 180 degrees.

0:08:38.430,0:08:43.222
So x plus 131 is equal to 180.

0:08:43.222,0:08:45.300
x is equal to what?

0:08:45.300,0:08:47.580
49 degrees.

0:08:47.580,0:08:49.190
There you go.

0:08:49.190,0:08:53.520
We've done the second[br]problem in the angle game.

0:08:53.520,0:08:56.230
I think that's all of the time[br]I have now in this video.

0:08:56.230,0:08:58.100
In the next video maybe I'll[br]do a couple more of these

0:08:58.100,0:08:59.600
angle game problems.

0:08:59.600,0:09:01.030
See you soon.