[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.93,0:00:03.63,Default,,0000,0000,0000,,Let's play the angle game.
Dialogue: 0,0:00:03.63,0:00:07.17,Default,,0000,0000,0000,,So I've drawn this crazy figure\Nhere and I'm going to give you
Dialogue: 0,0:00:07.17,0:00:09.59,Default,,0000,0000,0000,,a couple of angles and then I\Nwant you to figure
Dialogue: 0,0:00:09.59,0:00:10.95,Default,,0000,0000,0000,,out another angle.
Dialogue: 0,0:00:10.95,0:00:13.35,Default,,0000,0000,0000,,So let me give you some angles.
Dialogue: 0,0:00:13.35,0:00:24.97,Default,,0000,0000,0000,,So let's say that this angle\Nup here is 56 degrees.
Dialogue: 0,0:00:28.76,0:00:38.11,Default,,0000,0000,0000,,Then I also tell you this angle here is 115 degrees.
Dialogue: 0,0:00:41.86,0:00:46.02,Default,,0000,0000,0000,,What I would like you to figure out -- this is the object of
Dialogue: 0,0:00:46.02,0:00:50.04,Default,,0000,0000,0000,,the angle game -- I want you to\Nfigure out what this
Dialogue: 0,0:00:50.04,0:00:54.61,Default,,0000,0000,0000,,angle is - right here.
Dialogue: 0,0:00:55.36,0:00:59.31,Default,,0000,0000,0000,,If you are brave, you can pause the video and try to
Dialogue: 0,0:00:59.31,0:01:00.100,Default,,0000,0000,0000,,figure it out yourself.
Dialogue: 0,0:01:00.100,0:01:02.82,Default,,0000,0000,0000,,If you would like me to walk\Nyou through it -- and maybe I
Dialogue: 0,0:01:02.82,0:01:04.52,Default,,0000,0000,0000,,can give you a couple of steps\Nand then you pause it and you
Dialogue: 0,0:01:04.52,0:01:05.97,Default,,0000,0000,0000,,get the rest of it by yourself.
Dialogue: 0,0:01:05.97,0:01:08.41,Default,,0000,0000,0000,,But I will now show you\Nhow I would have solved
Dialogue: 0,0:01:08.41,0:01:10.81,Default,,0000,0000,0000,,this in the angle game.
Dialogue: 0,0:01:10.81,0:01:14.37,Default,,0000,0000,0000,,You have all the tools\Nnecessary to already solve it.
Dialogue: 0,0:01:14.37,0:01:16.42,Default,,0000,0000,0000,,I want you to be able to get\Ngood at this, because this is
Dialogue: 0,0:01:16.42,0:01:19.80,Default,,0000,0000,0000,,kind of like the key\Nskill on the SAT.
Dialogue: 0,0:01:19.80,0:01:22.08,Default,,0000,0000,0000,,Oh, I didn't give you a key\Npiece of -- you're probably
Dialogue: 0,0:01:22.08,0:01:23.56,Default,,0000,0000,0000,,saying I can't solve this.
Dialogue: 0,0:01:23.56,0:01:25.25,Default,,0000,0000,0000,,You probably can't because\NI haven't given you a key
Dialogue: 0,0:01:25.25,0:01:26.76,Default,,0000,0000,0000,,piece of information.
Dialogue: 0,0:01:26.76,0:01:29.51,Default,,0000,0000,0000,,This line here and this line\Nhere, so this line and this
Dialogue: 0,0:01:29.51,0:01:32.13,Default,,0000,0000,0000,,line, they're parallel.
Dialogue: 0,0:01:32.13,0:01:34.33,Default,,0000,0000,0000,,I was telling you to solve\Nit before giving you a
Dialogue: 0,0:01:34.33,0:01:35.29,Default,,0000,0000,0000,,key piece of information.
Dialogue: 0,0:01:35.29,0:01:37.12,Default,,0000,0000,0000,,That means that\Nthey are parallel.
Dialogue: 0,0:01:37.12,0:01:38.74,Default,,0000,0000,0000,,So what can we do this figure?
Dialogue: 0,0:01:38.74,0:01:41.50,Default,,0000,0000,0000,,So whenever I see these type of\Nproblems, either while playing
Dialogue: 0,0:01:41.50,0:01:46.89,Default,,0000,0000,0000,,the angle game or on, say, an\NSAT, I just literally kind of
Dialogue: 0,0:01:46.89,0:01:50.32,Default,,0000,0000,0000,,figure out every angle that I\Ncan figure out and slowly try
Dialogue: 0,0:01:50.32,0:01:53.57,Default,,0000,0000,0000,,to make my way to\Nthe goal angle.
Dialogue: 0,0:01:53.57,0:01:54.95,Default,,0000,0000,0000,,Let's see what we can\Nfigure out here.
Dialogue: 0,0:01:54.95,0:01:58.08,Default,,0000,0000,0000,,So I'm going to do it in this\Nblue-green color anything
Dialogue: 0,0:01:58.08,0:02:00.07,Default,,0000,0000,0000,,that I can figure out.
Dialogue: 0,0:02:00.07,0:02:04.26,Default,,0000,0000,0000,,So this angle is 56\Ndegrees, right?
Dialogue: 0,0:02:04.26,0:02:06.70,Default,,0000,0000,0000,,These lines are parallel.
Dialogue: 0,0:02:06.70,0:02:10.78,Default,,0000,0000,0000,,This line here looks like a transversal -- a transversal!
Dialogue: 0,0:02:10.78,0:02:12.46,Default,,0000,0000,0000,,So what do we know about it?
Dialogue: 0,0:02:12.46,0:02:14.68,Default,,0000,0000,0000,,Well, let's see, what's a corresponding angle to
Dialogue: 0,0:02:14.68,0:02:16.42,Default,,0000,0000,0000,,this angle right here?
Dialogue: 0,0:02:16.42,0:02:18.83,Default,,0000,0000,0000,,Well, it's the angle, right?
Dialogue: 0,0:02:18.83,0:02:21.25,Default,,0000,0000,0000,,What do we know about\Ncorresponding angles for
Dialogue: 0,0:02:21.25,0:02:23.85,Default,,0000,0000,0000,,parallel lines when you have a transversal?
Dialogue: 0,0:02:23.85,0:02:25.71,Default,,0000,0000,0000,,That's 56 degrees.
Dialogue: 0,0:02:26.88,0:02:30.38,Default,,0000,0000,0000,,56 degrees - right? Because corresponding angles are equal.
Dialogue: 0,0:02:30.38,0:02:31.77,Default,,0000,0000,0000,,We could have done a\Nlot of other stuff.
Dialogue: 0,0:02:31.77,0:02:33.73,Default,,0000,0000,0000,,We could have figured out that\Nthis angle is 56 degrees, but
Dialogue: 0,0:02:33.73,0:02:37.43,Default,,0000,0000,0000,,that probably wouldn't have\Ngotten us closer to our goal.
Dialogue: 0,0:02:37.43,0:02:40.15,Default,,0000,0000,0000,,That angle's 56 degrees and\Nits corresponding angle
Dialogue: 0,0:02:40.15,0:02:41.58,Default,,0000,0000,0000,,is also 56 degrees.
Dialogue: 0,0:02:41.58,0:02:43.46,Default,,0000,0000,0000,,That wouldn't have gotten\Nus any closer to our goal.
Dialogue: 0,0:02:43.46,0:02:46.91,Default,,0000,0000,0000,,We could have figured out that\Nthis is 180 minus 56, right,
Dialogue: 0,0:02:46.91,0:02:49.71,Default,,0000,0000,0000,,which is, what? 124 degrees.
Dialogue: 0,0:02:49.71,0:02:51.27,Default,,0000,0000,0000,,That really wouldn't\Nhave helped us much.
Dialogue: 0,0:02:51.27,0:02:53.54,Default,,0000,0000,0000,,I'm showing you, these are all\Nthings that you can do while
Dialogue: 0,0:02:53.54,0:02:54.87,Default,,0000,0000,0000,,playing the angle game.
Dialogue: 0,0:02:54.87,0:02:57.38,Default,,0000,0000,0000,,But anyway, the first step\N-- I said well, these are
Dialogue: 0,0:02:57.38,0:03:00.81,Default,,0000,0000,0000,,corresponding angles,\Nso that's 56 degrees.
Dialogue: 0,0:03:00.81,0:03:04.16,Default,,0000,0000,0000,,So let's see, I need to figure\Nout this angle right here.
Dialogue: 0,0:03:04.16,0:03:07.72,Default,,0000,0000,0000,,I know this one, and they're\Nin a triangle, right?
Dialogue: 0,0:03:07.72,0:03:09.12,Default,,0000,0000,0000,,You see this triangle.
Dialogue: 0,0:03:09.12,0:03:12.01,Default,,0000,0000,0000,,If only I knew this angle.
Dialogue: 0,0:03:13.96,0:03:16.03,Default,,0000,0000,0000,,Can you figure out this angle?
Dialogue: 0,0:03:16.91,0:03:22.41,Default,,0000,0000,0000,,Well, it is supplementary to\Nthis 115 degrees, right?
Dialogue: 0,0:03:22.42,0:03:24.92,Default,,0000,0000,0000,,So this green angle plus this purple angle
Dialogue: 0,0:03:24.92,0:03:29.39,Default,,0000,0000,0000,,is equal to 180. So this is 180 minus 115.
Dialogue: 0,0:03:29.39,0:03:33.57,Default,,0000,0000,0000,,So what's that? 180 minus -- so this\Nis 65 degrees.
Dialogue: 0,0:03:34.71,0:03:36.00,Default,,0000,0000,0000,,So what have we done so far?
Dialogue: 0,0:03:36.00,0:03:38.06,Default,,0000,0000,0000,,We just said well these\Nare parallel lines, so
Dialogue: 0,0:03:38.06,0:03:40.01,Default,,0000,0000,0000,,corresponding angles are equal.
Dialogue: 0,0:03:40.01,0:03:43.90,Default,,0000,0000,0000,,So this 56 degrees is\Nequal to this 56 degrees.
Dialogue: 0,0:03:43.90,0:03:47.24,Default,,0000,0000,0000,,Then we said, well, this green\Nangle and this purple angle are
Dialogue: 0,0:03:47.24,0:03:49.11,Default,,0000,0000,0000,,supplementary, so they\Nhave to add up to 180.
Dialogue: 0,0:03:49.11,0:03:51.01,Default,,0000,0000,0000,,So this is 115.
Dialogue: 0,0:03:51.01,0:03:55.87,Default,,0000,0000,0000,,But this is 65, which\Nis just 180 minus 115.
Dialogue: 0,0:03:55.87,0:03:57.69,Default,,0000,0000,0000,,I think you might see\Nwhere I'm going now.
Dialogue: 0,0:03:57.69,0:04:02.64,Default,,0000,0000,0000,,Now we know two angles\Nof a triangle.
Dialogue: 0,0:04:02.64,0:04:05.44,Default,,0000,0000,0000,,If we know two angles of a\Ntriangle, what can figure
Dialogue: 0,0:04:05.44,0:04:05.96,Default,,0000,0000,0000,,out about the third?
Dialogue: 0,0:04:05.96,0:04:09.87,Default,,0000,0000,0000,,Well, we know the angles of a\Ntriangle add up to 180, right?
Dialogue: 0,0:04:09.87,0:04:13.21,Default,,0000,0000,0000,,So let's called this x.
Dialogue: 0,0:04:13.21,0:04:23.35,Default,,0000,0000,0000,,We know that x plus 56\Nplus 65 equals 180.
Dialogue: 0,0:04:23.35,0:04:25.21,Default,,0000,0000,0000,,What's 56 plus 65?
Dialogue: 0,0:04:25.21,0:04:27.64,Default,,0000,0000,0000,,This is where I always\Nmess up, on the addition
Dialogue: 0,0:04:27.64,0:04:28.82,Default,,0000,0000,0000,,and the subtraction.
Dialogue: 0,0:04:28.82,0:04:32.34,Default,,0000,0000,0000,,So, 5 plus 6 is 110.
Dialogue: 0,0:04:32.34,0:04:35.71,Default,,0000,0000,0000,,This is 121 I believe.
Dialogue: 0,0:04:35.74,0:04:39.80,Default,,0000,0000,0000,,121, right? ... right, 121 equals 180.
Dialogue: 0,0:04:40.90,0:04:43.16,Default,,0000,0000,0000,,Then x is equal to --\Nlet's see, 180 minus
Dialogue: 0,0:04:43.16,0:04:46.04,Default,,0000,0000,0000,,20 is 60, so it's 59.
Dialogue: 0,0:04:46.04,0:04:49.46,Default,,0000,0000,0000,,x is equal to 59 degrees.
Dialogue: 0,0:04:52.37,0:04:53.70,Default,,0000,0000,0000,,There we go.
Dialogue: 0,0:04:53.70,0:04:59.22,Default,,0000,0000,0000,,We have accomplished our first\Ngoal in the angle game.
Dialogue: 0,0:04:59.22,0:05:00.32,Default,,0000,0000,0000,,There you saw it.
Dialogue: 0,0:05:00.32,0:05:03.00,Default,,0000,0000,0000,,So let's do a tougher\Nangle problem.
Dialogue: 0,0:05:06.39,0:05:09.54,Default,,0000,0000,0000,,This one maybe won't involve parallel lines.
Dialogue: 0,0:05:09.54,0:05:11.40,Default,,0000,0000,0000,,But I just want to show you,\Neverything really just boils
Dialogue: 0,0:05:11.40,0:05:15.28,Default,,0000,0000,0000,,down to everything we learned\Nabout parallel lines and
Dialogue: 0,0:05:15.28,0:05:18.34,Default,,0000,0000,0000,,triangles and angles\Nadding up to each other.
Dialogue: 0,0:05:18.34,0:05:20.81,Default,,0000,0000,0000,,So this one involves a star.
Dialogue: 0,0:05:22.44,0:05:24.73,Default,,0000,0000,0000,,Let me draw the star.
Dialogue: 0,0:05:24.73,0:05:27.96,Default,,0000,0000,0000,,So, let's see -- a line from there to there.
Dialogue: 0,0:05:27.96,0:05:30.40,Default,,0000,0000,0000,,Draw a line from there to there.
Dialogue: 0,0:05:30.73,0:05:33.36,Default,,0000,0000,0000,,Draw a line from there to there.
Dialogue: 0,0:05:33.62,0:05:36.52,Default,,0000,0000,0000,,Draw a line from there to there.
Dialogue: 0,0:05:37.19,0:05:39.84,Default,,0000,0000,0000,,Draw a line from there to there.
Dialogue: 0,0:05:39.84,0:05:41.51,Default,,0000,0000,0000,,What do we know about this?
Dialogue: 0,0:05:41.51,0:05:44.40,Default,,0000,0000,0000,,We know that this angle\Nis 75 -- oh boy, I'm
Dialogue: 0,0:05:44.40,0:05:45.41,Default,,0000,0000,0000,,using the wrong tool.
Dialogue: 0,0:05:45.41,0:05:48.75,Default,,0000,0000,0000,,This angle is 75 degrees.
Dialogue: 0,0:05:48.75,0:05:54.28,Default,,0000,0000,0000,,We also know that this\Nangle is 75 degrees.
Dialogue: 0,0:05:54.28,0:06:00.30,Default,,0000,0000,0000,,We know this angle\Nhere is 101 degrees.
Dialogue: 0,0:06:00.30,0:06:06.64,Default,,0000,0000,0000,,Your mission in this angle\Ngame is to figure out
Dialogue: 0,0:06:06.64,0:06:08.92,Default,,0000,0000,0000,,this angle right here.
Dialogue: 0,0:06:08.92,0:06:10.91,Default,,0000,0000,0000,,What is this angle?
Dialogue: 0,0:06:10.91,0:06:13.03,Default,,0000,0000,0000,,This is a good time to\Npause because I will now
Dialogue: 0,0:06:13.03,0:06:14.55,Default,,0000,0000,0000,,show you the solution.
Dialogue: 0,0:06:14.55,0:06:15.56,Default,,0000,0000,0000,,So what can we do here?
Dialogue: 0,0:06:15.56,0:06:19.23,Default,,0000,0000,0000,,So this angle, well jeez, I\Njust like to just mess around
Dialogue: 0,0:06:19.23,0:06:20.69,Default,,0000,0000,0000,,and see what I can figure out.
Dialogue: 0,0:06:20.69,0:06:23.80,Default,,0000,0000,0000,,So, if this angle here is\N101 degrees, what other
Dialogue: 0,0:06:23.80,0:06:24.88,Default,,0000,0000,0000,,angles can we figure out?
Dialogue: 0,0:06:24.88,0:06:27.55,Default,,0000,0000,0000,,We could figure out -- well, we\Ncould figure out this angle.
Dialogue: 0,0:06:27.55,0:06:28.54,Default,,0000,0000,0000,,We could figure out\Na bunch of angles.
Dialogue: 0,0:06:28.54,0:06:31.64,Default,,0000,0000,0000,,We could figure out that -- let\Nme switch the color, these
Dialogue: 0,0:06:31.64,0:06:33.72,Default,,0000,0000,0000,,are my "figure out" angles.
Dialogue: 0,0:06:33.72,0:06:37.01,Default,,0000,0000,0000,,So that's 101, then this\Nis supplementary, that's
Dialogue: 0,0:06:37.01,0:06:39.11,Default,,0000,0000,0000,,79 degrees, right?
Dialogue: 0,0:06:39.11,0:06:44.19,Default,,0000,0000,0000,,That's also 79 degrees because\Nthis is also supplementary.
Dialogue: 0,0:06:44.19,0:06:46.10,Default,,0000,0000,0000,,This angle right here is\Nopposite to it, so this
Dialogue: 0,0:06:46.10,0:06:49.49,Default,,0000,0000,0000,,angle right here is\Ngoing to be 101 degrees.
Dialogue: 0,0:06:51.95,0:06:54.37,Default,,0000,0000,0000,,What else can figure out?
Dialogue: 0,0:06:54.37,0:06:56.51,Default,,0000,0000,0000,,We could figure out this angle\Nbecause it's supplementary, we
Dialogue: 0,0:06:56.51,0:06:57.91,Default,,0000,0000,0000,,could figure out this angle.
Dialogue: 0,0:06:57.91,0:06:59.70,Default,,0000,0000,0000,,We could also figure out this\Nangle because we see this
Dialogue: 0,0:06:59.70,0:07:01.38,Default,,0000,0000,0000,,triangle right here.
Dialogue: 0,0:07:01.38,0:07:07.86,Default,,0000,0000,0000,,This angle plus 75 plus 75 is\Ngoing to equal 180, right?
Dialogue: 0,0:07:07.86,0:07:12.18,Default,,0000,0000,0000,,So let's call this\Nangle b, b for blue.
Dialogue: 0,0:07:12.18,0:07:19.91,Default,,0000,0000,0000,,So b plus 75 plus 75 is\Ngoing to equal 180.
Dialogue: 0,0:07:19.91,0:07:25.05,Default,,0000,0000,0000,,And I'm just using this\Ntriangle right here.
Dialogue: 0,0:07:25.05,0:07:33.20,Default,,0000,0000,0000,,So b plus 150 is equal to 180,\Nor b is equal to 30 degrees.
Dialogue: 0,0:07:33.20,0:07:35.96,Default,,0000,0000,0000,,So we're able to\Nfigure this out.
Dialogue: 0,0:07:35.96,0:07:38.37,Default,,0000,0000,0000,,Now, what will you do if I told you that
Dialogue: 0,0:07:38.37,0:07:41.28,Default,,0000,0000,0000,,we are now ready to figure out this yellow angle?
Dialogue: 0,0:07:41.28,0:07:42.26,Default,,0000,0000,0000,,It might not be obvious to you.
Dialogue: 0,0:07:42.26,0:07:43.96,Default,,0000,0000,0000,,You kind of have to look at the\Ntriangle in the right way, and
Dialogue: 0,0:07:43.96,0:07:46.85,Default,,0000,0000,0000,,the SAT will do this to you\Nall the time, all the time.
Dialogue: 0,0:07:46.85,0:07:49.17,Default,,0000,0000,0000,,That's why I'm testing\Nyou this way.
Dialogue: 0,0:07:49.17,0:07:51.74,Default,,0000,0000,0000,,Well, let me give you a little hint:
Dialogue: 0,0:07:51.74,0:07:53.74,Default,,0000,0000,0000,,Look at this triangle.
Dialogue: 0,0:07:55.65,0:07:59.72,Default,,0000,0000,0000,,Non-ideal color, let me do it in red so it really stands out.
Dialogue: 0,0:08:00.36,0:08:02.59,Default,,0000,0000,0000,,Look at this triangle.
Dialogue: 0,0:08:02.59,0:08:04.29,Default,,0000,0000,0000,,I'll tell you, the hardest\Nthing about these problems is
Dialogue: 0,0:08:04.29,0:08:07.14,Default,,0000,0000,0000,,just looking at the right\Ntriangle and kind of seeing
Dialogue: 0,0:08:07.14,0:08:11.26,Default,,0000,0000,0000,,that oh wow, I actually\Ncan figure out something.
Dialogue: 0,0:08:11.26,0:08:14.80,Default,,0000,0000,0000,,Look at this triangle\Nright here.
Dialogue: 0,0:08:14.80,0:08:17.38,Default,,0000,0000,0000,,We know this angle\Nof it, 101 degrees.
Dialogue: 0,0:08:17.38,0:08:19.04,Default,,0000,0000,0000,,We know this angle, we\Njust figured it out,
Dialogue: 0,0:08:19.04,0:08:20.97,Default,,0000,0000,0000,,it was 30 degrees.
Dialogue: 0,0:08:20.97,0:08:23.21,Default,,0000,0000,0000,,So all we have left is to\Nfigure out this yellow
Dialogue: 0,0:08:23.21,0:08:25.31,Default,,0000,0000,0000,,angle, call it x.
Dialogue: 0,0:08:28.80,0:08:35.49,Default,,0000,0000,0000,,So x plus 101 ... plus 30 is equal to 180 degrees because
Dialogue: 0,0:08:35.49,0:08:38.43,Default,,0000,0000,0000,,the angles in a triangle\Nadd up to 180 degrees.
Dialogue: 0,0:08:38.43,0:08:43.22,Default,,0000,0000,0000,,So x plus 131 is equal to 180.
Dialogue: 0,0:08:43.22,0:08:45.30,Default,,0000,0000,0000,,x is equal to what?
Dialogue: 0,0:08:45.30,0:08:47.58,Default,,0000,0000,0000,,49 degrees.
Dialogue: 0,0:08:47.58,0:08:49.19,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:08:49.19,0:08:53.52,Default,,0000,0000,0000,,We've done the second\Nproblem in the angle game.
Dialogue: 0,0:08:53.52,0:08:56.23,Default,,0000,0000,0000,,I think that's all of the time\NI have now in this video.
Dialogue: 0,0:08:56.23,0:08:58.10,Default,,0000,0000,0000,,In the next video maybe I'll\Ndo a couple more of these
Dialogue: 0,0:08:58.10,0:08:59.60,Default,,0000,0000,0000,,angle game problems.
Dialogue: 0,0:08:59.60,0:09:01.03,Default,,0000,0000,0000,,See you soon.