WEBVTT 00:00:00.930 --> 00:00:03.630 Let's play the angle game. 00:00:03.630 --> 00:00:07.170 So I've drawn this crazy figure here and I'm going to give you 00:00:07.170 --> 00:00:09.590 a couple of angles and then I want you to figure 00:00:09.590 --> 00:00:10.950 out another angle. 00:00:10.950 --> 00:00:13.350 So let me give you some angles. 00:00:13.350 --> 00:00:24.970 So let's say that this angle up here is 56 degrees. 00:00:28.755 --> 00:00:38.108 Then I also tell you this angle here is 115 degrees. 00:00:41.862 --> 00:00:46.016 What I would like you to figure out -- this is the object of 00:00:46.016 --> 00:00:50.040 the angle game -- I want you to figure out what this 00:00:50.040 --> 00:00:54.606 angle is - right here. 00:00:55.360 --> 00:00:59.313 If you are brave, you can pause the video and try to 00:00:59.313 --> 00:01:00.997 figure it out yourself. 00:01:00.997 --> 00:01:02.815 If you would like me to walk you through it -- and maybe I 00:01:02.815 --> 00:01:04.520 can give you a couple of steps and then you pause it and you 00:01:04.520 --> 00:01:05.970 get the rest of it by yourself. 00:01:05.970 --> 00:01:08.410 But I will now show you how I would have solved 00:01:08.410 --> 00:01:10.810 this in the angle game. 00:01:10.810 --> 00:01:14.370 You have all the tools necessary to already solve it. 00:01:14.370 --> 00:01:16.420 I want you to be able to get good at this, because this is 00:01:16.420 --> 00:01:19.800 kind of like the key skill on the SAT. 00:01:19.800 --> 00:01:22.080 Oh, I didn't give you a key piece of -- you're probably 00:01:22.080 --> 00:01:23.560 saying I can't solve this. 00:01:23.560 --> 00:01:25.250 You probably can't because I haven't given you a key 00:01:25.250 --> 00:01:26.760 piece of information. 00:01:26.760 --> 00:01:29.510 This line here and this line here, so this line and this 00:01:29.510 --> 00:01:32.130 line, they're parallel. 00:01:32.130 --> 00:01:34.330 I was telling you to solve it before giving you a 00:01:34.330 --> 00:01:35.290 key piece of information. 00:01:35.290 --> 00:01:37.120 That means that they are parallel. 00:01:37.120 --> 00:01:38.740 So what can we do this figure? 00:01:38.740 --> 00:01:41.500 So whenever I see these type of problems, either while playing 00:01:41.500 --> 00:01:46.890 the angle game or on, say, an SAT, I just literally kind of 00:01:46.890 --> 00:01:50.320 figure out every angle that I can figure out and slowly try 00:01:50.320 --> 00:01:53.570 to make my way to the goal angle. 00:01:53.570 --> 00:01:54.950 Let's see what we can figure out here. 00:01:54.950 --> 00:01:58.080 So I'm going to do it in this blue-green color anything 00:01:58.080 --> 00:02:00.070 that I can figure out. 00:02:00.070 --> 00:02:04.260 So this angle is 56 degrees, right? 00:02:04.260 --> 00:02:06.700 These lines are parallel. 00:02:06.700 --> 00:02:10.781 This line here looks like a transversal -- a transversal! 00:02:10.781 --> 00:02:12.464 So what do we know about it? 00:02:12.464 --> 00:02:14.685 Well, let's see, what's a corresponding angle to 00:02:14.685 --> 00:02:16.420 this angle right here? 00:02:16.420 --> 00:02:18.830 Well, it's the angle, right? 00:02:18.830 --> 00:02:21.248 What do we know about corresponding angles for 00:02:21.248 --> 00:02:23.848 parallel lines when you have a transversal? 00:02:23.848 --> 00:02:25.710 That's 56 degrees. 00:02:26.875 --> 00:02:30.375 56 degrees - right? Because corresponding angles are equal. 00:02:30.375 --> 00:02:31.768 We could have done a lot of other stuff. 00:02:31.768 --> 00:02:33.730 We could have figured out that this angle is 56 degrees, but 00:02:33.730 --> 00:02:37.430 that probably wouldn't have gotten us closer to our goal. 00:02:37.430 --> 00:02:40.150 That angle's 56 degrees and its corresponding angle 00:02:40.150 --> 00:02:41.580 is also 56 degrees. 00:02:41.580 --> 00:02:43.460 That wouldn't have gotten us any closer to our goal. 00:02:43.460 --> 00:02:46.910 We could have figured out that this is 180 minus 56, right, 00:02:46.910 --> 00:02:49.710 which is, what? 124 degrees. 00:02:49.710 --> 00:02:51.270 That really wouldn't have helped us much. 00:02:51.270 --> 00:02:53.540 I'm showing you, these are all things that you can do while 00:02:53.540 --> 00:02:54.870 playing the angle game. 00:02:54.870 --> 00:02:57.380 But anyway, the first step -- I said well, these are 00:02:57.380 --> 00:03:00.810 corresponding angles, so that's 56 degrees. 00:03:00.810 --> 00:03:04.160 So let's see, I need to figure out this angle right here. 00:03:04.160 --> 00:03:07.720 I know this one, and they're in a triangle, right? 00:03:07.720 --> 00:03:09.120 You see this triangle. 00:03:09.120 --> 00:03:12.008 If only I knew this angle. 00:03:13.962 --> 00:03:16.032 Can you figure out this angle? 00:03:16.910 --> 00:03:22.410 Well, it is supplementary to this 115 degrees, right? 00:03:22.425 --> 00:03:24.924 So this green angle plus this purple angle 00:03:24.924 --> 00:03:29.393 is equal to 180. So this is 180 minus 115. 00:03:29.393 --> 00:03:33.570 So what's that? 180 minus -- so this is 65 degrees. 00:03:34.709 --> 00:03:36.002 So what have we done so far? 00:03:36.002 --> 00:03:38.060 We just said well these are parallel lines, so 00:03:38.060 --> 00:03:40.010 corresponding angles are equal. 00:03:40.010 --> 00:03:43.900 So this 56 degrees is equal to this 56 degrees. 00:03:43.900 --> 00:03:47.240 Then we said, well, this green angle and this purple angle are 00:03:47.240 --> 00:03:49.110 supplementary, so they have to add up to 180. 00:03:49.110 --> 00:03:51.010 So this is 115. 00:03:51.010 --> 00:03:55.870 But this is 65, which is just 180 minus 115. 00:03:55.870 --> 00:03:57.690 I think you might see where I'm going now. 00:03:57.690 --> 00:04:02.640 Now we know two angles of a triangle. 00:04:02.640 --> 00:04:05.440 If we know two angles of a triangle, what can figure 00:04:05.440 --> 00:04:05.960 out about the third? 00:04:05.960 --> 00:04:09.870 Well, we know the angles of a triangle add up to 180, right? 00:04:09.870 --> 00:04:13.210 So let's called this x. 00:04:13.210 --> 00:04:23.350 We know that x plus 56 plus 65 equals 180. 00:04:23.350 --> 00:04:25.210 What's 56 plus 65? 00:04:25.210 --> 00:04:27.635 This is where I always mess up, on the addition 00:04:27.635 --> 00:04:28.820 and the subtraction. 00:04:28.820 --> 00:04:32.340 So, 5 plus 6 is 110. 00:04:32.340 --> 00:04:35.713 This is 121 I believe. 00:04:35.744 --> 00:04:39.798 121, right? ... right, 121 equals 180. 00:04:40.900 --> 00:04:43.160 Then x is equal to -- let's see, 180 minus 00:04:43.160 --> 00:04:46.040 20 is 60, so it's 59. 00:04:46.040 --> 00:04:49.462 x is equal to 59 degrees. 00:04:52.370 --> 00:04:53.701 There we go. 00:04:53.701 --> 00:04:59.215 We have accomplished our first goal in the angle game. 00:04:59.215 --> 00:05:00.321 There you saw it. 00:05:00.321 --> 00:05:03.005 So let's do a tougher angle problem. 00:05:06.390 --> 00:05:09.536 This one maybe won't involve parallel lines. 00:05:09.536 --> 00:05:11.400 But I just want to show you, everything really just boils 00:05:11.400 --> 00:05:15.280 down to everything we learned about parallel lines and 00:05:15.280 --> 00:05:18.340 triangles and angles adding up to each other. 00:05:18.340 --> 00:05:20.811 So this one involves a star. 00:05:22.442 --> 00:05:24.730 Let me draw the star. 00:05:24.730 --> 00:05:27.959 So, let's see -- a line from there to there. 00:05:27.959 --> 00:05:30.405 Draw a line from there to there. 00:05:30.728 --> 00:05:33.362 Draw a line from there to there. 00:05:33.624 --> 00:05:36.515 Draw a line from there to there. 00:05:37.192 --> 00:05:39.840 Draw a line from there to there. 00:05:39.840 --> 00:05:41.510 What do we know about this? 00:05:41.510 --> 00:05:44.400 We know that this angle is 75 -- oh boy, I'm 00:05:44.400 --> 00:05:45.410 using the wrong tool. 00:05:45.410 --> 00:05:48.750 This angle is 75 degrees. 00:05:48.750 --> 00:05:54.280 We also know that this angle is 75 degrees. 00:05:54.280 --> 00:06:00.300 We know this angle here is 101 degrees. 00:06:00.300 --> 00:06:06.640 Your mission in this angle game is to figure out 00:06:06.640 --> 00:06:08.920 this angle right here. 00:06:08.920 --> 00:06:10.910 What is this angle? 00:06:10.910 --> 00:06:13.030 This is a good time to pause because I will now 00:06:13.030 --> 00:06:14.550 show you the solution. 00:06:14.550 --> 00:06:15.560 So what can we do here? 00:06:15.560 --> 00:06:19.230 So this angle, well jeez, I just like to just mess around 00:06:19.230 --> 00:06:20.690 and see what I can figure out. 00:06:20.690 --> 00:06:23.800 So, if this angle here is 101 degrees, what other 00:06:23.800 --> 00:06:24.880 angles can we figure out? 00:06:24.880 --> 00:06:27.550 We could figure out -- well, we could figure out this angle. 00:06:27.550 --> 00:06:28.540 We could figure out a bunch of angles. 00:06:28.540 --> 00:06:31.640 We could figure out that -- let me switch the color, these 00:06:31.640 --> 00:06:33.720 are my "figure out" angles. 00:06:33.720 --> 00:06:37.010 So that's 101, then this is supplementary, that's 00:06:37.010 --> 00:06:39.110 79 degrees, right? 00:06:39.110 --> 00:06:44.190 That's also 79 degrees because this is also supplementary. 00:06:44.190 --> 00:06:46.100 This angle right here is opposite to it, so this 00:06:46.100 --> 00:06:49.487 angle right here is going to be 101 degrees. 00:06:51.948 --> 00:06:54.372 What else can figure out? 00:06:54.372 --> 00:06:56.510 We could figure out this angle because it's supplementary, we 00:06:56.510 --> 00:06:57.910 could figure out this angle. 00:06:57.910 --> 00:06:59.700 We could also figure out this angle because we see this 00:06:59.700 --> 00:07:01.380 triangle right here. 00:07:01.380 --> 00:07:07.860 This angle plus 75 plus 75 is going to equal 180, right? 00:07:07.860 --> 00:07:12.180 So let's call this angle b, b for blue. 00:07:12.180 --> 00:07:19.910 So b plus 75 plus 75 is going to equal 180. 00:07:19.910 --> 00:07:25.050 And I'm just using this triangle right here. 00:07:25.050 --> 00:07:33.200 So b plus 150 is equal to 180, or b is equal to 30 degrees. 00:07:33.200 --> 00:07:35.960 So we're able to figure this out. 00:07:35.960 --> 00:07:38.366 Now, what will you do if I told you that 00:07:38.366 --> 00:07:41.280 we are now ready to figure out this yellow angle? 00:07:41.280 --> 00:07:42.260 It might not be obvious to you. 00:07:42.260 --> 00:07:43.965 You kind of have to look at the triangle in the right way, and 00:07:43.965 --> 00:07:46.850 the SAT will do this to you all the time, all the time. 00:07:46.850 --> 00:07:49.170 That's why I'm testing you this way. 00:07:49.170 --> 00:07:51.740 Well, let me give you a little hint: 00:07:51.740 --> 00:07:53.740 Look at this triangle. 00:07:55.647 --> 00:07:59.717 Non-ideal color, let me do it in red so it really stands out. 00:08:00.360 --> 00:08:02.590 Look at this triangle. 00:08:02.590 --> 00:08:04.290 I'll tell you, the hardest thing about these problems is 00:08:04.290 --> 00:08:07.140 just looking at the right triangle and kind of seeing 00:08:07.140 --> 00:08:11.260 that oh wow, I actually can figure out something. 00:08:11.260 --> 00:08:14.800 Look at this triangle right here. 00:08:14.800 --> 00:08:17.380 We know this angle of it, 101 degrees. 00:08:17.380 --> 00:08:19.040 We know this angle, we just figured it out, 00:08:19.040 --> 00:08:20.970 it was 30 degrees. 00:08:20.970 --> 00:08:23.210 So all we have left is to figure out this yellow 00:08:23.210 --> 00:08:25.313 angle, call it x. 00:08:28.805 --> 00:08:35.490 So x plus 101 ... plus 30 is equal to 180 degrees because 00:08:35.490 --> 00:08:38.430 the angles in a triangle add up to 180 degrees. 00:08:38.430 --> 00:08:43.222 So x plus 131 is equal to 180. 00:08:43.222 --> 00:08:45.300 x is equal to what? 00:08:45.300 --> 00:08:47.580 49 degrees. 00:08:47.580 --> 00:08:49.190 There you go. 00:08:49.190 --> 00:08:53.520 We've done the second problem in the angle game. 00:08:53.520 --> 00:08:56.230 I think that's all of the time I have now in this video. 00:08:56.230 --> 00:08:58.100 In the next video maybe I'll do a couple more of these 00:08:58.100 --> 00:08:59.600 angle game problems. 00:08:59.600 --> 00:09:01.030 See you soon.