[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.01,0:00:02.00,Default,,0000,0000,0000,,Welcome back.
Dialogue: 0,0:00:02.00,0:00:04.83,Default,,0000,0000,0000,,Let's do a couple more angle\Ngame problems, and hopefully
Dialogue: 0,0:00:04.83,0:00:07.75,Default,,0000,0000,0000,,this will make you an\Nangle game expert.
Dialogue: 0,0:00:07.75,0:00:11.71,Default,,0000,0000,0000,,So let's start, I have the star\Ndrawn again, and let's say we
Dialogue: 0,0:00:11.71,0:00:13.12,Default,,0000,0000,0000,,know the following angles.
Dialogue: 0,0:00:13.12,0:00:18.32,Default,,0000,0000,0000,,We know this angle right\Nhere is 41 degrees.
Dialogue: 0,0:00:21.14,0:00:25.71,Default,,0000,0000,0000,,We know this angle\Nhere is 113 degrees.
Dialogue: 0,0:00:29.96,0:00:35.92,Default,,0000,0000,0000,,We know this angle\Nhere is 101 degrees.
Dialogue: 0,0:00:35.92,0:00:40.07,Default,,0000,0000,0000,,And what we have to figure out\N-- this is the goal of this
Dialogue: 0,0:00:40.07,0:00:44.36,Default,,0000,0000,0000,,angle game -- we want to figure\Nout what this angle is.
Dialogue: 0,0:00:44.36,0:00:48.30,Default,,0000,0000,0000,,And like always, I encourage\Nyou to try it on your own.
Dialogue: 0,0:00:48.30,0:00:51.50,Default,,0000,0000,0000,,Pause the video and then just\Ntry to work it through.
Dialogue: 0,0:00:51.50,0:00:54.52,Default,,0000,0000,0000,,If you get stuck, then play\Nthe video again and hopefully
Dialogue: 0,0:00:54.52,0:00:56.45,Default,,0000,0000,0000,,I'll have a solution for you.
Dialogue: 0,0:00:56.45,0:00:59.30,Default,,0000,0000,0000,,So pause right now, but\Notherwise let me explain
Dialogue: 0,0:00:59.30,0:01:00.30,Default,,0000,0000,0000,,how to do this.
Dialogue: 0,0:01:00.30,0:01:02.90,Default,,0000,0000,0000,,So let's see, we know this,\Nthis and this, and we're going
Dialogue: 0,0:01:02.90,0:01:05.74,Default,,0000,0000,0000,,to figure out this angle.
Dialogue: 0,0:01:05.74,0:01:07.06,Default,,0000,0000,0000,,So how can we figure\Nout this angle?
Dialogue: 0,0:01:07.06,0:01:08.49,Default,,0000,0000,0000,,What are the possible\Nstrategies?
Dialogue: 0,0:01:08.49,0:01:10.85,Default,,0000,0000,0000,,Well, if we knew this\Nangle here, we could say
Dialogue: 0,0:01:10.85,0:01:12.14,Default,,0000,0000,0000,,they're supplementary.
Dialogue: 0,0:01:12.14,0:01:14.06,Default,,0000,0000,0000,,But that angle seems like a\Nhard angle to figure out
Dialogue: 0,0:01:14.06,0:01:16.61,Default,,0000,0000,0000,,too, because it's not a\Npart of any triangles.
Dialogue: 0,0:01:16.61,0:01:19.26,Default,,0000,0000,0000,,But this angle is a\Npart of this triangle
Dialogue: 0,0:01:19.26,0:01:20.55,Default,,0000,0000,0000,,right here, right?
Dialogue: 0,0:01:20.55,0:01:23.94,Default,,0000,0000,0000,,So if we were able to figure\Nout this angle and this angle,
Dialogue: 0,0:01:23.94,0:01:26.54,Default,,0000,0000,0000,,these green angles, if we're\Nable to figure out these green
Dialogue: 0,0:01:26.54,0:01:32.84,Default,,0000,0000,0000,,angles, then we could figure\Nout this brown angle, which is
Dialogue: 0,0:01:32.84,0:01:35.29,Default,,0000,0000,0000,,the goal of this angle game.
Dialogue: 0,0:01:35.29,0:01:37.92,Default,,0000,0000,0000,,So, this could also be a good\Ntime to pause because I
Dialogue: 0,0:01:37.92,0:01:40.39,Default,,0000,0000,0000,,just gave you a hint.
Dialogue: 0,0:01:40.39,0:01:43.93,Default,,0000,0000,0000,,This green angle, well it's\Nsupplementary to this angle
Dialogue: 0,0:01:43.93,0:01:47.30,Default,,0000,0000,0000,,right here, so that means it\Nadds up to 180 degrees, and
Dialogue: 0,0:01:47.30,0:01:49.73,Default,,0000,0000,0000,,that's clear because it's\Non kind of the same line.
Dialogue: 0,0:01:49.73,0:01:52.18,Default,,0000,0000,0000,,So this is 101 degrees\Nand this is going to
Dialogue: 0,0:01:52.18,0:01:53.90,Default,,0000,0000,0000,,be 79 degrees, right?
Dialogue: 0,0:01:53.90,0:01:56.51,Default,,0000,0000,0000,,So it adds up to 180 degrees.
Dialogue: 0,0:01:56.51,0:01:58.89,Default,,0000,0000,0000,,That's 79.
Dialogue: 0,0:01:58.89,0:02:03.48,Default,,0000,0000,0000,,Now how can we figure\Nout this angle?
Dialogue: 0,0:02:03.48,0:02:07.73,Default,,0000,0000,0000,,Well, it's kind of left by\Nitself out in the corner of
Dialogue: 0,0:02:07.73,0:02:10.22,Default,,0000,0000,0000,,some place, so we could see if\Nit's part of any triangles.
Dialogue: 0,0:02:10.22,0:02:13.03,Default,,0000,0000,0000,,But we already said it's\Npart of this triangle.
Dialogue: 0,0:02:13.03,0:02:14.37,Default,,0000,0000,0000,,But that doesn't help us\Nbecause we don't know
Dialogue: 0,0:02:14.37,0:02:16.33,Default,,0000,0000,0000,,this angle and that's\Nactually our goal.
Dialogue: 0,0:02:16.33,0:02:18.56,Default,,0000,0000,0000,,What other triangles\Nis it a part of?
Dialogue: 0,0:02:18.56,0:02:21.54,Default,,0000,0000,0000,,Well, it's a part of this\Ntriangle right here.
Dialogue: 0,0:02:21.54,0:02:24.12,Default,,0000,0000,0000,,That's why I like the star\Nproblem because it has all
Dialogue: 0,0:02:24.12,0:02:26.19,Default,,0000,0000,0000,,these triangles in it that\Nmight not be obvious to you the
Dialogue: 0,0:02:26.19,0:02:27.88,Default,,0000,0000,0000,,first time you look at it.
Dialogue: 0,0:02:27.88,0:02:29.30,Default,,0000,0000,0000,,But the more you look at you\Nsee all these triangles.
Dialogue: 0,0:02:29.30,0:02:31.76,Default,,0000,0000,0000,,So it's part of this\Ntriangle, and it's also
Dialogue: 0,0:02:31.76,0:02:33.89,Default,,0000,0000,0000,,part of this triangle.
Dialogue: 0,0:02:33.89,0:02:38.06,Default,,0000,0000,0000,,I'm going to draw this triangle\Nanother color because I think
Dialogue: 0,0:02:38.06,0:02:40.26,Default,,0000,0000,0000,,it'll be clear to you that this\Nis a useful triangle to see
Dialogue: 0,0:02:40.26,0:02:41.02,Default,,0000,0000,0000,,that's it's a part of.
Dialogue: 0,0:02:55.67,0:02:57.18,Default,,0000,0000,0000,,So we have that triangle.
Dialogue: 0,0:02:57.18,0:02:59.79,Default,,0000,0000,0000,,So do we know two of the\Nangles of that triangle?
Dialogue: 0,0:02:59.79,0:03:00.23,Default,,0000,0000,0000,,Well sure.
Dialogue: 0,0:03:00.23,0:03:02.79,Default,,0000,0000,0000,,We know this angle and\Nwe know this angle.
Dialogue: 0,0:03:02.79,0:03:07.74,Default,,0000,0000,0000,,So we know that this angle plus\N113 plus 41 is going to equal
Dialogue: 0,0:03:07.74,0:03:11.05,Default,,0000,0000,0000,,180 degrees because of the\Nthree angles of a triangle.
Dialogue: 0,0:03:11.05,0:03:15.87,Default,,0000,0000,0000,,So let me call this, I\Ndon't know, g for green.
Dialogue: 0,0:03:18.61,0:03:20.85,Default,,0000,0000,0000,,Let's call this g for green.
Dialogue: 0,0:03:20.85,0:03:28.97,Default,,0000,0000,0000,,So we know g plus 113 degrees,\Nthat's this one right here,
Dialogue: 0,0:03:28.97,0:03:32.80,Default,,0000,0000,0000,,plus 41 -- remember, we're\Nlooking at this triangle;
Dialogue: 0,0:03:32.80,0:03:34.81,Default,,0000,0000,0000,,that's the hardest part just\Nkeeping track of which triangle
Dialogue: 0,0:03:34.81,0:03:39.97,Default,,0000,0000,0000,,we're looking at -- is\Ngoing to equal 180 degrees.
Dialogue: 0,0:03:39.97,0:03:46.30,Default,,0000,0000,0000,,g plus, what is this, 154?
Dialogue: 0,0:03:46.30,0:03:46.58,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:03:46.58,0:03:51.14,Default,,0000,0000,0000,,40, 50, 154 equals 180 degrees.
Dialogue: 0,0:03:51.14,0:03:53.17,Default,,0000,0000,0000,,That's always where I\Nmess up on the addition.
Dialogue: 0,0:03:53.17,0:03:57.20,Default,,0000,0000,0000,,And so g is equal to, what is\Nthis, 26 degrees, right,
Dialogue: 0,0:03:57.20,0:03:59.51,Default,,0000,0000,0000,,because I just subtract\N154 from both sides.
Dialogue: 0,0:04:02.79,0:04:03.89,Default,,0000,0000,0000,,So we're almost there.
Dialogue: 0,0:04:03.89,0:04:05.94,Default,,0000,0000,0000,,So we figured out g, we\Nknow this green angle.
Dialogue: 0,0:04:05.94,0:04:07.43,Default,,0000,0000,0000,,We just have to figure out\Nthis, and they're all part
Dialogue: 0,0:04:07.43,0:04:10.49,Default,,0000,0000,0000,,of this triangle, this\Nsmall one right here.
Dialogue: 0,0:04:10.49,0:04:13.57,Default,,0000,0000,0000,,This small triangle.
Dialogue: 0,0:04:13.57,0:04:17.46,Default,,0000,0000,0000,,So our goal, which is\Nlet's call this x.
Dialogue: 0,0:04:17.46,0:04:21.91,Default,,0000,0000,0000,,x plus g, which is 26 degrees\N-- we just figured that out.
Dialogue: 0,0:04:21.91,0:04:26.82,Default,,0000,0000,0000,,26 plus this angle, 79 -- and\Nwe figured that out because it
Dialogue: 0,0:04:26.82,0:04:29.01,Default,,0000,0000,0000,,was supplementary to this\Nangle -- is going to
Dialogue: 0,0:04:29.01,0:04:31.32,Default,,0000,0000,0000,,equal 180 degrees.
Dialogue: 0,0:04:31.32,0:04:38.54,Default,,0000,0000,0000,,So x plus, what is this,\N105 equal to 180.
Dialogue: 0,0:04:38.54,0:04:43.00,Default,,0000,0000,0000,,So x is equal to 75 degrees,\Nif I did my addition and
Dialogue: 0,0:04:43.00,0:04:44.53,Default,,0000,0000,0000,,subtraction correctly.
Dialogue: 0,0:04:44.53,0:04:49.66,Default,,0000,0000,0000,,So x is equal to 75 degrees.
Dialogue: 0,0:04:49.66,0:04:51.52,Default,,0000,0000,0000,,And then we are done.
Dialogue: 0,0:04:51.52,0:04:53.94,Default,,0000,0000,0000,,Let's do another one\Nof these problems.
Dialogue: 0,0:04:53.94,0:04:55.30,Default,,0000,0000,0000,,And these problems are all\Ngenerated on the
Dialogue: 0,0:04:55.30,0:04:58.22,Default,,0000,0000,0000,,Khan Academy website, dynamically\Nby the computer.
Dialogue: 0,0:04:58.22,0:05:01.40,Default,,0000,0000,0000,,Whoever wrote this software\Nmust be a genius.
Dialogue: 0,0:05:01.40,0:05:02.53,Default,,0000,0000,0000,,But anyway, back\Nto the problems.
Dialogue: 0,0:05:07.11,0:05:09.55,Default,,0000,0000,0000,,Let me draw some more.
Dialogue: 0,0:05:09.55,0:05:13.79,Default,,0000,0000,0000,,So this is going to be a pretty\Nstraightforward drawing.
Dialogue: 0,0:05:13.79,0:05:18.27,Default,,0000,0000,0000,,It's pretty much just two\Ntriangles next to each other.
Dialogue: 0,0:05:18.27,0:05:20.86,Default,,0000,0000,0000,,Like that and then let me draw\Nanother line that goes like
Dialogue: 0,0:05:20.86,0:05:24.16,Default,,0000,0000,0000,,that, and then we draw a line\Nthat goes like that, and I
Dialogue: 0,0:05:24.16,0:05:25.94,Default,,0000,0000,0000,,think I have done my drawing.
Dialogue: 0,0:05:25.94,0:05:27.06,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:05:27.06,0:05:28.59,Default,,0000,0000,0000,,I'm have done my drawing.
Dialogue: 0,0:05:28.59,0:05:30.00,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:05:30.00,0:05:32.61,Default,,0000,0000,0000,,What do we know about this\Ntriangle and what do
Dialogue: 0,0:05:32.61,0:05:34.96,Default,,0000,0000,0000,,we need to figure out?
Dialogue: 0,0:05:34.96,0:05:39.96,Default,,0000,0000,0000,,I'm going to tell you that this\Nangle here, this big angle
Dialogue: 0,0:05:39.96,0:05:42.50,Default,,0000,0000,0000,,here, is 86 degrees.
Dialogue: 0,0:05:46.36,0:05:50.36,Default,,0000,0000,0000,,We also know that this\Nangle here is 28 degrees.
Dialogue: 0,0:05:54.15,0:06:00.59,Default,,0000,0000,0000,,And we also know that this\Nangle here is 122 degrees.
Dialogue: 0,0:06:00.59,0:06:04.81,Default,,0000,0000,0000,,And our goal, our mission\Nin this round is to figure
Dialogue: 0,0:06:04.81,0:06:06.39,Default,,0000,0000,0000,,out what this angle is.
Dialogue: 0,0:06:06.39,0:06:08.67,Default,,0000,0000,0000,,And maybe we can do it, we\Ncan do it in a good color.
Dialogue: 0,0:06:08.67,0:06:12.56,Default,,0000,0000,0000,,Maybe we can do it in a\Ncouple of different ways.
Dialogue: 0,0:06:12.56,0:06:17.72,Default,,0000,0000,0000,,So one thing we could do is we\Ncould figure out what this
Dialogue: 0,0:06:17.72,0:06:20.47,Default,,0000,0000,0000,,angle is, so we could just\Nsubtract this green angle from
Dialogue: 0,0:06:20.47,0:06:23.27,Default,,0000,0000,0000,,86 and we would get our answer.
Dialogue: 0,0:06:23.27,0:06:25.94,Default,,0000,0000,0000,,Well, this angle's easy, right,\Nbecause we know two angles
Dialogue: 0,0:06:25.94,0:06:28.39,Default,,0000,0000,0000,,of this triangle, so we\Ncould figure that out.
Dialogue: 0,0:06:28.39,0:06:30.73,Default,,0000,0000,0000,,Let's just call this, I don't\Nknow, let's call this y.
Dialogue: 0,0:06:30.73,0:06:41.90,Default,,0000,0000,0000,,So y plus 122 plus 28 degrees\Nis going to equal 180.
Dialogue: 0,0:06:41.90,0:06:48.42,Default,,0000,0000,0000,,So y plus 150 is equal to 180.
Dialogue: 0,0:06:48.42,0:06:51.17,Default,,0000,0000,0000,,So y is equal to 30\Ndegrees, right?
Dialogue: 0,0:06:51.17,0:06:55.78,Default,,0000,0000,0000,,So this is equal to 30 degrees.
Dialogue: 0,0:06:55.78,0:06:59.98,Default,,0000,0000,0000,,So this is 30 degrees, and\Nthis big angle here is 86.
Dialogue: 0,0:06:59.98,0:07:06.13,Default,,0000,0000,0000,,So our goal, let's call that x,\Nso x is going to just be equal
Dialogue: 0,0:07:06.13,0:07:11.23,Default,,0000,0000,0000,,to the big angle, 86 minus this\Nangle we just figured
Dialogue: 0,0:07:11.23,0:07:14.20,Default,,0000,0000,0000,,out, minus 30.
Dialogue: 0,0:07:14.20,0:07:17.43,Default,,0000,0000,0000,,So x is going to be\Nequal to 50 degrees.
Dialogue: 0,0:07:17.43,0:07:17.83,Default,,0000,0000,0000,,Done.
Dialogue: 0,0:07:17.83,0:07:19.86,Default,,0000,0000,0000,,That was a pretty\Nstraightforward problem.
Dialogue: 0,0:07:19.86,0:07:22.26,Default,,0000,0000,0000,,Let's see if we could figure\Nthat out any other way.
Dialogue: 0,0:07:22.26,0:07:25.96,Default,,0000,0000,0000,,Well, we could say instead\Nof doing it that way --
Dialogue: 0,0:07:25.96,0:07:28.49,Default,,0000,0000,0000,,let's forget we just\Nsolved it that way.
Dialogue: 0,0:07:28.49,0:07:33.66,Default,,0000,0000,0000,,We could say this angle here\Nis supplementary to this
Dialogue: 0,0:07:33.66,0:07:37.23,Default,,0000,0000,0000,,122 degree angle, right, so\Nit has to add up to 180.
Dialogue: 0,0:07:37.23,0:07:41.18,Default,,0000,0000,0000,,So this plus 122 is 180, so\Nwhat does that make this?
Dialogue: 0,0:07:41.18,0:07:46.39,Default,,0000,0000,0000,,It makes this 58\Ndegrees, right?
Dialogue: 0,0:07:46.39,0:07:47.83,Default,,0000,0000,0000,,This plus this is\Ngoing to be 180.
Dialogue: 0,0:07:47.83,0:07:49.04,Default,,0000,0000,0000,,So we figured out this.
Dialogue: 0,0:07:49.04,0:07:50.74,Default,,0000,0000,0000,,If we could figure out\Nthis, then we could
Dialogue: 0,0:07:50.74,0:07:52.19,Default,,0000,0000,0000,,use this triangle.
Dialogue: 0,0:07:52.19,0:07:54.80,Default,,0000,0000,0000,,How do we figure\Nout this angle?
Dialogue: 0,0:07:54.80,0:08:02.34,Default,,0000,0000,0000,,Well, we could look at this big\Ntriangle here, and we know
Dialogue: 0,0:08:02.34,0:08:06.54,Default,,0000,0000,0000,,this side, right, and we\Ncould figure out this.
Dialogue: 0,0:08:06.54,0:08:08.41,Default,,0000,0000,0000,,Let's call this z.
Dialogue: 0,0:08:08.41,0:08:14.13,Default,,0000,0000,0000,,So we know that z plus this\Nangle, plus 28, plus this big
Dialogue: 0,0:08:14.13,0:08:18.62,Default,,0000,0000,0000,,angle, plus 86 is equal to 180.
Dialogue: 0,0:08:18.62,0:08:26.07,Default,,0000,0000,0000,,So z plus, what is this,\N106, 114 is equal to 180.
Dialogue: 0,0:08:26.07,0:08:30.45,Default,,0000,0000,0000,,So z is equal to, what\Nis this, 66 degrees.
Dialogue: 0,0:08:30.45,0:08:32.25,Default,,0000,0000,0000,,I don't know if I'm doing\Nany of my math correctly,
Dialogue: 0,0:08:32.25,0:08:33.77,Default,,0000,0000,0000,,but let's just hope.
Dialogue: 0,0:08:33.77,0:08:35.58,Default,,0000,0000,0000,,z equals 66.
Dialogue: 0,0:08:35.58,0:08:41.00,Default,,0000,0000,0000,,So z is 66, this angle is 58,\Nand now we can use this
Dialogue: 0,0:08:41.00,0:08:47.96,Default,,0000,0000,0000,,triangle here to figure out\Nwhat this angle is, our x.
Dialogue: 0,0:08:47.96,0:09:00.84,Default,,0000,0000,0000,,So x plus 66 plus 58\Nis equal to 180.
Dialogue: 0,0:09:00.84,0:09:03.44,Default,,0000,0000,0000,,I already think I might\Nhave made a mistake some
Dialogue: 0,0:09:03.44,0:09:04.15,Default,,0000,0000,0000,,place in the addition.
Dialogue: 0,0:09:04.15,0:09:08.08,Default,,0000,0000,0000,,So this time around I get x\Nis equal to -- let's see,
Dialogue: 0,0:09:08.08,0:09:13.60,Default,,0000,0000,0000,,66 plus 58 is 110 plus 14.
Dialogue: 0,0:09:13.60,0:09:17.11,Default,,0000,0000,0000,,So 180 minus 124.
Dialogue: 0,0:09:17.11,0:09:21.60,Default,,0000,0000,0000,,So now I got it, x is\Nequal to 56 degrees.
Dialogue: 0,0:09:21.60,0:09:23.35,Default,,0000,0000,0000,,Oh great, I actually\Ngot the right answer.
Dialogue: 0,0:09:23.35,0:09:24.50,Default,,0000,0000,0000,,I was looking at this, I\Nthought it was 50, but this
Dialogue: 0,0:09:24.50,0:09:26.79,Default,,0000,0000,0000,,was 56, right -- 86 minus 30.
Dialogue: 0,0:09:26.79,0:09:29.15,Default,,0000,0000,0000,,So x is equal to\N56 degrees again.
Dialogue: 0,0:09:29.15,0:09:30.42,Default,,0000,0000,0000,,So we did it two\Ndifferent ways.
Dialogue: 0,0:09:30.42,0:09:31.11,Default,,0000,0000,0000,,That's what I wanted\Nto show you.
Dialogue: 0,0:09:31.11,0:09:32.79,Default,,0000,0000,0000,,There's actually not a right\Nanswer, as long as you kind
Dialogue: 0,0:09:32.79,0:09:34.97,Default,,0000,0000,0000,,of get there eventually.
Dialogue: 0,0:09:34.97,0:09:36.90,Default,,0000,0000,0000,,We solved it two different ways\Nand I did all my addition and
Dialogue: 0,0:09:36.90,0:09:40.94,Default,,0000,0000,0000,,subtraction correctly, and you\Nget the exact same answer.
Dialogue: 0,0:09:40.94,0:09:45.73,Default,,0000,0000,0000,,So hopefully you find the angle\Ngame fun and you'll be playing
Dialogue: 0,0:09:45.73,0:09:47.00,Default,,0000,0000,0000,,this with your friends.
Dialogue: 0,0:09:47.00,0:09:48.64,Default,,0000,0000,0000,,I'll see you later.