1 00:00:00,670 --> 00:00:08,020 Let's do this question, or a regular polygon with nine diagonals find the internal angle and external 2 00:00:08,020 --> 00:00:09,600 angle was the video. 3 00:00:09,610 --> 00:00:11,560 Give it a try and then let's do it together. 4 00:00:12,220 --> 00:00:12,640 All right. 5 00:00:12,640 --> 00:00:13,090 We're back. 6 00:00:13,120 --> 00:00:14,350 I hope you've given it a try. 7 00:00:14,620 --> 00:00:15,720 Let's do it together. 8 00:00:16,510 --> 00:00:19,700 Say, in is the number of sites of the polygon. 9 00:00:20,170 --> 00:00:27,940 Now, we are given that the number of diagonals is equal to nine, we have NC to minus in is equal to 10 00:00:27,940 --> 00:00:30,730 nine C permutation and combination S.. 11 00:00:30,950 --> 00:00:32,440 For more details for this. 12 00:00:32,830 --> 00:00:33,280 All right. 13 00:00:33,430 --> 00:00:34,500 What does NC do? 14 00:00:34,630 --> 00:00:40,140 That's in the end minus one by two and that minus in gives you nine. 15 00:00:40,360 --> 00:00:46,360 Now instead of forming a quadratic equation and solving four nine, it's faster if you just do trial 16 00:00:46,360 --> 00:00:46,830 and error. 17 00:00:46,870 --> 00:00:47,200 Right. 18 00:00:47,470 --> 00:00:50,890 So let's do a few trial and error operations. 19 00:00:51,080 --> 00:00:52,630 Let's take in as ten. 20 00:00:52,930 --> 00:00:55,000 In that case, what would be this? 21 00:00:55,300 --> 00:00:57,160 This is in in nine. 22 00:00:57,160 --> 00:00:57,540 Right. 23 00:00:57,970 --> 00:01:03,080 That's ten in the nine divided by two minus ten almost. 24 00:01:03,080 --> 00:01:03,990 Do you get that. 25 00:01:04,000 --> 00:01:07,330 Forty five minus ten which is equal to thirty five. 26 00:01:07,610 --> 00:01:13,990 So if anything the number of diagonals is 35, but we have only nine diagonals so it has to be less 27 00:01:13,990 --> 00:01:14,590 than ten. 28 00:01:14,590 --> 00:01:14,930 Right. 29 00:01:15,100 --> 00:01:17,110 So let's take and is equal to seven. 30 00:01:17,120 --> 00:01:18,490 What do we get in this case. 31 00:01:20,060 --> 00:01:24,770 If any is equal to seven, you will see that you will get the answer as 14, right? 32 00:01:24,800 --> 00:01:28,220 What is that, seven into six by two minus seven. 33 00:01:28,560 --> 00:01:32,120 Over here you have twenty one minus seven, which is 14. 34 00:01:32,340 --> 00:01:34,410 So that again is greater than nine. 35 00:01:34,580 --> 00:01:36,590 So let's try and is equal to six. 36 00:01:36,590 --> 00:01:40,270 In that case, it would be six in the five by two minus six. 37 00:01:40,580 --> 00:01:43,280 So you get 15 minus six which is equal to nine. 38 00:01:43,520 --> 00:01:46,310 The N is equal to six, gives you nine diagonals. 39 00:01:46,520 --> 00:01:52,080 Therefore the number of sides of this polygon is equal to six. 40 00:01:52,100 --> 00:01:54,700 So we are dealing with the hexagon already. 41 00:01:54,980 --> 00:01:58,160 Now what is the sum of internal angles of a polygon? 42 00:01:58,400 --> 00:02:03,410 It's in minus two in two 180 right now because it's a regular polygon. 43 00:02:03,420 --> 00:02:05,270 What would be each internal angle? 44 00:02:05,480 --> 00:02:08,730 It is in minus two into 180 divided by in. 45 00:02:09,080 --> 00:02:12,140 Now let's apply and is equal to six over here. 46 00:02:12,410 --> 00:02:15,320 Will we get four into 180 divided by six. 47 00:02:15,500 --> 00:02:15,920 Right. 48 00:02:16,160 --> 00:02:18,490 That is equal to 120. 49 00:02:19,190 --> 00:02:24,890 Therefore, the internal angle of this polygon is equal to 120 degree. 50 00:02:25,190 --> 00:02:29,570 Now we know that the internal and external angle of the polygon are supplementary. 51 00:02:29,750 --> 00:02:31,600 That is, they add up to 180 degrees. 52 00:02:31,850 --> 00:02:37,910 Therefore, the external angle is equal to 180 minus 120, which is equal to 60 degrees.