WEBVTT 1 00:00:00.256 --> 00:00:02.560 Welcome to Brainfuse! 2 00:00:04.608 --> 00:00:10.752 In this lesson, we are working with polygons and we're asked to find the measure of one 3 00:00:11.008 --> 00:00:16.384 Central angle and one interior angle in the regular polygon below. 4 00:00:17.920 --> 00:00:22.784 So, before we get started we need to review a few of these terms. First of all: 5 00:00:23.040 --> 00:00:27.648 Polygon. So "poly-" is a Greek root that means "many," 6 00:00:27.904 --> 00:00:29.440 And 7 00:00:29.696 --> 00:00:33.280 This word means "many-sided." 8 00:00:34.048 --> 00:00:39.027 So polygons are made up of line segments that join to create a 9 00:00:39.027 --> 00:00:41.472 Many-sided closed figure. 10 00:00:41.728 --> 00:00:44.544 Those can include triangles, 11 00:00:44.800 --> 00:00:49.920 Quadrilaterals, and after that they usually have a name that follows 12 00:00:50.176 --> 00:00:51.968 Certain guidelines. 13 00:00:52.224 --> 00:00:52.736 We'll call it 14 00:00:53.760 --> 00:00:57.344 An "n-gon," where the shape ends with 15 00:00:57.600 --> 00:01:03.744 The suffix -gon and "n" stands for a Greek prefix that tells us 16 00:01:04.000 --> 00:01:10.144 How many sides the shape has. So for example, let's look at this polygon. And it has one, 17 00:01:10.400 --> 00:01:17.056 Two, three, four, five, six sides; so it is called a hexagon. 18 00:01:17.056 --> 00:01:17.056 19 00:01:19.872 --> 00:01:22.688 And "hexa-" is a Greek root meaning "six." 20 00:01:24.224 --> 00:01:29.097 This polygon is also called a regular polygon. 21 00:01:29.097 --> 00:01:31.392 So what makes it regular? 22 00:01:31.392 --> 00:01:33.696 As you can see with the tick marks, its 23 00:01:33.696 --> 00:01:36.768 sides are equal in length 24 00:01:36.768 --> 00:01:42.400 and also its interior angles, which we'll soon find out about, 25 00:01:42.400 --> 00:01:44.192 are equal. 26 00:01:58.784 --> 00:02:04.928 Next, we have central angle and then we'll review exactly what the interior angles are. 27 00:02:04.928 --> 00:02:11.328 Central angle: As you can see, a regular polygon can be broken up into triangles. 28 00:02:11.328 --> 00:02:11.328 29 00:02:11.840 --> 00:02:14.656 And these lines that meet in the center form 30 00:02:14.912 --> 00:02:16.704 Central angles. 31 00:02:20.544 --> 00:02:26.688 Okay, as you can see, these angles all add up to 360 degrees because 32 00:02:26.688 --> 00:02:28.992 they form a circle when put together. 33 00:02:29.248 --> 00:02:32.320 And the interior angles: 34 00:02:34.624 --> 00:02:38.208 They're the angle created when two line segments meet. 35 00:02:40.768 --> 00:02:46.400 We'll start with the central angle and move on to the interior. 36 00:02:46.656 --> 00:02:48.448 Now for the central, 37 00:02:50.752 --> 00:02:55.872 You'll notice that when we drew arcs to represent each central angle they formed 38 00:02:56.128 --> 00:02:58.688 a complete circle. So the sum of 39 00:02:59.200 --> 00:03:03.552 all central angles in a regular polygon is 360 degrees. 40 00:03:07.904 --> 00:03:14.048 But this problem is asking for just one central angle. So what we need to do is divide it by n, 41 00:03:14.304 --> 00:03:18.144 where n is the number of sides. So in this case it's a hexagon, 42 00:03:18.400 --> 00:03:23.008 so we have six sides. So 360 43 00:03:24.032 --> 00:03:26.336 Degrees divided by 6 44 00:03:26.592 --> 00:03:29.664 Equals 60 degrees. 45 00:03:29.664 --> 00:03:29.664 46 00:03:31.200 --> 00:03:34.016 The measure of one central angle 47 00:03:35.808 --> 00:03:38.368 So let's say we're working with this central angle 48 00:03:38.624 --> 00:03:41.440 Is equal to 60 degrees. 49 00:03:44.256 --> 00:03:48.352 Now let's move to the interior angles. 50 00:03:55.008 --> 00:03:58.080 I'll add "angles" here just for symmetry. 51 00:04:01.664 --> 00:04:07.808 For interior angles: this also has a formula that we can follow, and here it is. 52 00:04:14.976 --> 00:04:19.584 This formula gives us the sum of all interior angles. 53 00:04:19.839 --> 00:04:23.424 So for example, take a triangle. 54 00:04:24.704 --> 00:04:26.752 There are three sides in a triangle 55 00:04:27.008 --> 00:04:29.056 So 3 minus 2 is 1, 56 00:04:32.640 --> 00:04:38.784 Times 180, equals 180 degrees, the sum of interior angles in a triangle. 57 00:04:39.296 --> 00:04:42.368 In this case we have a hexagon 58 00:04:42.368 --> 00:04:42.368 59 00:04:42.624 --> 00:04:44.416 So there are six sides 60 00:04:44.672 --> 00:04:46.976 So we do 6 minus 2 61 00:04:47.488 --> 00:04:53.376 times 180 degrees. And that is 4 times 180 62 00:04:53.632 --> 00:04:55.936 720 degrees. 63 00:04:57.728 --> 00:05:00.032 And does this answer the question? 64 00:05:00.800 --> 00:05:05.664 Well, it says find the measure of one central angle and one interior angle. 65 00:05:05.920 --> 00:05:10.784 So we need one, that means we divide by the number of sides 66 00:05:11.040 --> 00:05:12.576 in our polygon. 67 00:05:13.088 --> 00:05:19.232 So 720 degrees divided by 6 equals 120 degrees. 68 00:05:24.302 --> 00:05:24.302 69 00:05:24.302 --> 00:05:27.169 Each interior angle is equal to 70 00:05:27.169 --> 00:05:30.496 120 degrees in a hexagon. 71 00:05:31.520 --> 00:05:37.664 If you'd like to work on more of these problems, please click on Live Help to work with a Brainfuse tutor. 72 00:05:37.920 --> 00:05:46.875 Making flashcards with the Greek prefixes on them will also help you identify each polygon you see. Thanks for watching this lesson.