Math Puzzles Quiz | IQ Test

[00:00:40]All right guys, this is the very first question for today. We need to solve for the red region area and you are going to give your answer in terms of y. Give your answer in exact form. Take your time. Think about it. Let's see how many of can do this.

[00:00:57]Let's see who's going to give the answer first.

[00:02:28]Hi Kushra, thanks for joining. So guys, we are solving for red reason area.

[00:02:35]Be quick with this one.

[00:02:42]I go see we are given with the circle and we can see that this arc or we can say circular arc has the radius of one unit and we need to solve for this reason area that is the red region area.

[00:03:00]Take your time think about it and give your answer in exact form. You are going to give your answer in terms of five.

[00:03:04]Don't give your answer in decimals.

[00:03:17]So guys, anyone with the correct answer for this?

[00:04:13]Guys, you have taken so much of time for this. It has been more than 4 minutes already.

[00:04:20]No one has given the answer for this.

[00:04:43]All right, we have one user C2Y is saying 4 minus Y. Anyone with the same answer or any explanation for this one that how we are going to approach for this?

[00:04:58]Okay, is also saying the same.

[00:05:11]All right. So, we'll not waste that much of time. 4 minus by let's see two of the user has already given the answer. Let's see if it is correct or not. And how we going to approach for this? See first of all if I can see if I'm going to join this these centers what I'm going to have they will pass through the common point of contact for sure right this like this I can join this and now see I'm going to have a square here and for this square all of the sides are going to be of two units because the radius is one so up to here this is one this is one so 1 + 1 is going to give me two so this side length is going to be of two units And now I have the square. I can solve for the area of the square. The area of the square is going to be 2 square which is going to be four minus area of these four quadrants. And of these four quadrants together will make a circle only. Right? So I can use pi r². What is the radius of every single quadrant? The radius is going to be one only. Right? So it's p<unk> 1 square which is going to be pi only. So 4 - pi is the final answer final exact answer for this question. So C2Y and Pagra are the only two users to give the answer for this question. We'll move to the next. Let's have the next one and let's see how many you can do that. Just give me a minute. I'll give you an easy one this time.

[00:06:40]Uh just uh let's have this 156. So we need to solve for the blue shaded area here also.

[00:06:54]Let's see who is going to give the correct answer for this. You are going to give your final answer in terms of pi only. Don't give your answer in decimals. Please be quick with this one.

[00:08:16]guys. Anyone with the correct answer for this? You're solving for blue shaded area and you are going to give your answer in terms of pi only.

[00:08:26]We have pw pw is saying 36 - 7 pi All right, let's just wait for a few more participants to participate.

[00:08:48]Okay, we have Kashag group. Shagra is saying the same. Yuko is saying the same. Alifa Ali is also saying the same. 36 - 7 pi.

[00:08:57]Let's see if it is correct or not. And See what I'm going to do? I can see that this is a square of side six units. So first of all, I'll solve for the area of the square which is going to be six square. And this will give you 36. Now what else you can see? You have four semicircle 1 2 3 and this four. And every semicircle has the diameter of 2 units. Therefore the radius of the semicircle is going to be one. Now four semicircles together will form two circles. So I'll be using the area of the two circles instead of writing the area for four semicircles. So 2 pi r² where radius is one only. So I'll be writing it as 2 pi only. Okay. Let's come back to quadrant. Now how many quadrants are there? 1 2 3 and four.

[00:09:43]Four quadrants in there. Every single quadrant has the radius of two units.

[00:09:48]Right? So instead of writing for four quadrants, I can use the area of the circle for that. So pi r² I'll be using where the radius of the quadrant is 2 square. So this will become 4 pi only.

[00:10:00]Now we are left with the circle only.

[00:10:01]The circle the diameter of the circle is also two. Therefore the radius is going to be 1 and the area is going to be p<unk> 1 square which will give you pi only. So subtract that pi also. So this 2 pi 4 pi and 1 pi together will become 7 pi. So 36 - 7 pi is the correct answer.

[00:10:20]So uh we have PW Kushadra, Yuko and Ali.

[00:10:25]You guys were correct. Uh Devil I hope it is clear to you. 36 - 7 pi is the right answer. It's not 36 - 10 pi. We'll have the next one. Then let's have this one.

[00:10:42]See here also we need to solve for the blue shaded area.

[00:10:47]We are given with the regular polygon.

[00:10:49]You can see that it's a hexagon and there are different sectors.

[00:10:56]Sectors of same size. We can see six different sectors are there. So give your answer in exact form. Don't give your answer in decimal. Let's see who's going to give the correct answer first.

[00:11:15]Eco friends your answer for the previous question is correct. But we are at the next question right now. You can be fresh yourself.

[00:13:11]guys anyone that's solving for blue shaded You're going to give your answer in terms of pi in exact form. Don't give your answer in decimals.

[00:15:12]guys. Anyone for this?

[00:15:18]It has been more than 3 minutes already.

[00:15:21]You guys have taken so much of time for this.

[00:15:25]Anyone use it to give the answer for this one?

[00:15:51]All right, we have PW. PW is saying 54 <unk>3 - 18 pi.

[00:16:01]Okay, we have Zen Zener is saying 16 uh 32.

[00:16:09]Okay, we'll see if it is correct or not.

[00:16:27]We have run run saying 54 <unk>3 - 18.

[00:16:33]Ali is also saying the same. Hi Zena.

[00:16:36]Okay, let's see guys if it is correct or not. Let's see what is the correct answer then.

[00:16:42]See first of all I can solve for the area of the hexagon which is the area of this entire figure. Correct? Now for hexagon you can divide the hexagon in six equal triangle. You can use the formula directly for the area of the hexagon which is going to be 3 <unk>3x2 side square right or can you you or you can divide the hexagon in six equal triangle. You can do that also. I'm using the direct formula here. So the side of the hexagon is already there which is six. So I'll be writing it as 6 square and on simplification this will give you 54 <unk>3. So I'm writing it here 54 <unk>3 for the area of the entire hexagon. Now what else I can do?

[00:17:23]I need to subtract all of these sectors, right? How many sectors are there? There are six sectors and every sector is substanding an angle of 120° because every single corner angle of a hexagon is of 120°. I know that. And 120° is nothing but 1/3 of a circle. Right? So there are six total sectors. So 6 into 1x3 pi r² for like 1x 3 p<unk> r² is for the area of the one sector and there are total six sectors. Right? So this is going to be two. So I can use like 2 pi r² which is the area of the two circles and the radius of every single sector is going to be of three units because side is six. This is going to be 3 three right? So the radius is going to be three. I'll be substituting it here 3 square. So 3 square into 2 will become 18 pi. So 18 pi is the unshaded area and I need to subtract it from the total reason area. So 54 pi 54 <unk>3 minus 18 pi is the right answer. So I can see like eco has given the correct explanation. Run your answer is correct.

[00:18:27]Ali your answer is correct.

[00:18:30]And pw your answer is also correct. 54 <unk>3 - 18 pi on simplification will give you something nearly 36 something.

[00:18:39]It's not going to be 16 uh uh 32. So I hope it is clear to everyone. We'll move to the next 54 <unk>3 - 18 pi is the correct answer.

[00:18:51]Let's have the next one. Just give me a minute.

[00:19:05]All right guys, this is very easy.

[00:19:08]Please be quick with this one. Once again, we need to solve for the shared reason area. Everything is given to you.

[00:19:14]So this is way more easier than the other questions we have discussed today. So be quick with this one.

[00:20:38]All right, we have BW, Yuko, Kushak and Killer David is also saying all of them are saying 10 cm square.

[00:20:48]Okay, let's just wait for a few more participants. Ali is saying 10 <unk>2.

[00:20:54]Okay, we'll see if it is correct or not.

[00:20:59]Anyone else?

[00:21:04]Guys, there are multiple approaches to this one and I'm going to show the one only.

[00:21:09]See, you can either solve for the entire area and subtract the bases shaded in an area. But I'm not doing that because I can divide the entire figure in five squares, right? You can see that. So these are nothing but the five squares. And if this is one, this is also one. I can solve for this side of the square like this one. The using the Pythagorean theorem. This is 1 square 1 square. This is going to give me roo<unk>2 root. So this side is going to be of roo<unk>2 units. And you can check that if this is <unk>2 this is also <unk>2 <unk>2 square + <unk>2 square will give you four which is the square of two. So it is validating right. So we have the side side of the square. Therefore the area of the every single square is going to be of two units. This is also two. This is two. This is two and this is two. So 2 into 5 will give you 10 as the final answer. So 10 square units or I can say 10 cm square is the answer for the shaded area. Jukes your answer is correct. Your explanation is also correct.

[00:22:16]So juke scaler debit and uh pushag yuko and pw you guys were correct. We'll have the next one then. Let's see how many of you can do that. Just give me a minute.

[00:22:46]Okay, this is very easy guys. We need to solve for the value of x here. We are going to solve for this missing angle.

[00:22:52]Please be quick with this one. We need to solve for the value of x. There are multiple approaches to this one also.

[00:22:59]Please be quick.

[00:23:04]Six is not the right answer for the previous question. 10 is the correct answer for the previous one. You can check your logic.

[00:23:39]Eco friend is saying 20. Uh you can have a look onto the angle that angle ais definitely is optim angle.

[00:23:52]20 is clearly an incorrect answer for the sun.

[00:23:57]Please check your Okay, we have Subhashi saying 150.

[00:24:28]Yuko is saying 130.

[00:24:31]All right, three users with three different answer. Let's just wait for a few more participants to answer this.

[00:25:12]All right. One more user bring 5070 is saying 160.

[00:25:20]Move is also saying 160. Kushag is saying 130. Guys, everyone is giving different answer. We have four different answer for this question. 120, 160, 130, and 160.

[00:25:29]Please check your logic. Once again, I'm saying this is not that easy. You're making mistakes somewhere.

[00:25:49]Is saying 160 and it's easy, but the answer is still incorrect.

[00:26:08]Okay, we have B PO B2F saying 80. Four different answers.

[00:26:17]Gret is saying 135. Fifth answer 160.

[00:26:26]I don't know how you guys are getting 160. Let's see now you eco is also saying 160.

[00:26:38]One more user with Unice. Ununice is saying 130. So most of the user are saying 130 and 160.

[00:26:44]Let's make it clearly Caesar is also saying 130.

[00:26:54]All right, let's see here. I'm going to tell you I'm going to drop the explanation. See here, guys. First of all, there are multiple approaches to this one. What I what I'm going to do, I'm going to extend this further.

[00:27:06]Now, I can see there I'm having a triangle here and this is 60°. I can solve for this angle. First of all, this is going to be 120°. And similarly, if this is 120°, I can solve for this angle. They are vertical angles, right?

[00:27:18]This is also going to be 20. Now for this smaller triangle, I have two of the interior angle. I can solve for the exterior angle. Exterior angle is equal to sum of the two interior angle. And this is 120 + 20. So 120 + 20 is going to give me 140. So now I have this angle 140. I'll focus on this region of the figure. And here I can see how many corner angles I'm having. This, this, this, this, and this. So there are five corner angles. This is a pentagon and sum of all the interior angles for a five-sided polygon is going to be 540.

[00:27:53]How many right angles I can see? This is 1 2 and 3. So directly I'm writing 3 into 90 270 for the right angles plus this 140 plus x and this is equals to 540. I can subtract 500 140 from 540 directly to get 400.

[00:28:13]And this 400 minus 270 when I'm going to take this 270 on another side I'll be getting the value of x as 130°.

[00:28:21]So 130° is the correct answer. 160 is completely incorrect. 140 is incorrect.

[00:28:26]80 is incorrect.

[00:28:30]135 is incorrect.

[00:28:34]150 is incorrect.

[00:28:39]It's 130.

[00:28:41]130° is the final answer guys. You can check your logic once again. So I can see how many of Yuko is the first one to give the correct answer for this one. Push at number two.

[00:28:54]Then saying 160 and then we have Philip saying 130. Uni saying 130. Julius Caesar is correct 130.

[00:29:05]Hameed is saying 130. Joshua Williams saying 130.

[00:29:10]Eco friend now corrected himself to 130.

[00:29:13]G wishal 130 is the right answer. Okay.

[00:29:16]So I hope it is clear to everyone now.

[00:29:18]130 is the right answer, not 160. We'll have the next one. Let's have the next one. Just give me a minute.

[00:29:32]Okay, let's have this.

[00:29:34]Now we need to solve for the missing angle which is this angle.

[00:29:42]L 160 is incorrect. I already delivered the explanation for this. 160 is the right answer. You can check your logic.

[00:29:49]We need to solve for this missing angle.

[00:29:52]We are having two different circles.

[00:29:56]Please be quick with this one. We are solving for this missing angle. And if possible you can drop your explanation and reason for your answers.

[00:31:14]Guys, we are solving for the missing angle.

[00:31:28]Please be quick with this one. We are taking so much of time for this. This is easy.

[00:32:20]Okay, we have one user PW is saying 25.

[00:32:25]Anyone else?

[00:32:29]Ishag is here saying 15. Okay, two users with two different answers. Anyone else, guys?

[00:32:58]Okay, Yuko is also saying 15. PW corrected himself to 115 only. Okay, three users are saying 15. Let's see if 15 is correct or not. See, there are multiple approaches we can use. Uh the property that uh the opposite angle of the cyclic quadrator are supplementary.

[00:33:17]But I'm not using that. I'm using the exterior angle property that the exterior angle of the cyclic coordinator this which is going to be this angle.

[00:33:24]This is going to be the interior angle made by the opposite internal segments.

[00:33:30]Right? So this is going to be like these are the segments opposite segments to this angle exterior angle and the angle made by these opposite segment is 55°.

[00:33:42]So this exterior angle is going to be equal to that. This is the property of the cyclic coordinate. So this is 55.

[00:33:50]Similarly, this angle I can solve for this angle. This is going to be 70° because this is 70. Correct? This is an exterior angle. Exterior angle is equal to the interior angle made by the opposite segments. So this is 70. This I can write this as 70.

[00:34:08]Now let's write keep it as I'm writing it here. See here also if I'm going to look at this figure I'm erasing this.

[00:34:16]This is also a cyclic quadillator and this is going to be an exterior angle for this cyclic quadrator. So this exterior angle is equal to this angle and this was 55 I has already written.

[00:34:28]So this is also going to be 55 and this angle is 70. Now let's just zoom it out.

[00:34:35]This is something like this. This is the missing angle we need to calculate. This is 55 and this is 70.

[00:34:42]So now I have the two interior angles where the missing angle plus 55 is going to be an exterior angle because sum of the two interior angle is equal to an exterior angle. So therefore the missing angle is going to be 70 minus 55 and the value of the missing angle is going to be 15°. So 15° is the correct answer.

[00:35:01]Pushup and pw you guys were correct.

[00:35:05]We'll have the next one. Just give me a minute.

[00:35:09]Let's have this.

[00:35:14]We need to solve for the missing angle which is this angle alpha.

[00:35:24]This angle. Take your time. Think about it. Let's see how many of can do this.

[00:35:30]There are multiple approaches to this one also. Please be quick.

[00:35:40]R 430715 is the right answer for the previous question. We are at the next question right now where we are solving for the missing angle alpha.

[00:35:52]Please be quick with this one. Let's see how many you can do this.

[00:36:05]Moa 7141 I can see like this is this angle which is alpha Right.

[00:36:35]Angle P. You can see we are solving for the measure of angle P.

[00:36:41]I hope it is clear.

[00:36:44]This is the missing angle. We need to calculate this angle. Let me write it here. Angle P. I hope now it is fine.

[00:36:59]Mohammed Zil 130 is not the correct answer for this one. Please.

[00:37:59]Okay. Is FE and AB are parallel? Okay.

[00:38:03]Let me see where is F.

[00:38:06]Yes, F and AB are definitely parallel.

[00:38:10]This is a regular polygon. This is a regular octagon. You can see the marking at the angles. So the opposite sides are definitely going to be par to each other. So we have PW saying 70. We have Witb is saying 35.

[00:38:26]Moa 7141 is saying 70. Two users saying 70. One is saying 35.

[00:38:39]Anyone else?

[00:38:47]Pushagra is saying 70.

[00:38:50]Okay. Most of the user are saying 70.

[00:38:53]Only one user has given the answer as 35.

[00:38:59]Yuko is also saying 70.

[00:39:03]Okay, let's see.

[00:39:05]See, I as I already mentioned, there are multiple approaches to this one. I'm going to show you the one only. See uh what I can see is if I'm going to draw a line here join F to B definitely this is going to be a right angle for sure right I can solve for this entire angle like this this one every single angle for the octagon is going to be of 135° right so if this is 90 I'm going to left with this angle and this much angle is going to be of 45° So let me write it as 45. Okay. Now see this is 135 entirely. This is 40. I can solve for this missing angle. Right?

[00:39:50]This is going to be of 5°. Now 45 + 5 entirely will become 50. So this angle is of 50°. I'm writing it here.

[00:39:58]Similarly if I'm going to look this side this entire angle is of 135°, right?

[00:40:04]This is 30. I can solve for the corner angle here also which is angle P E D.

[00:40:09]This is going to be of 15°.

[00:40:12]Just give me a minute.

[00:40:15]Okay, I'm talking about this angle now.

[00:40:16]This is 15°. So 15 + 45, this entire angle is going to be of 60°.

[00:40:24]So this is 60. This is 50. I can solve for this angle. Considering the triangle P E, I can solve for the angle P or I can say for the angle alpha. So alpha + 60 + 50 is equals to 180°. And from here on simplification I'll be getting the value of alpha the missing angle as 70°.

[00:40:51]70° is the right answer. Can't hardly hear.

[00:40:59]Okay.

[00:41:02]70 is the correct answer guys. I hope it is clear.

[00:41:11]Am I not audible guys?

[00:41:18]Julius, your answer is correct.

[00:41:22]70 is the correct answer.

[00:41:29]So I hope it is clear to everyone. We'll move to the next.

[00:41:33]Let's have the next one.

[00:42:00]S270 is the correct answer. We'll have this one. This is very easy. We need to solve for the value of X here. Please be quick with this one.

[00:42:15]Let's see who's going to give the correct answer first.

[00:42:52]Okay, one user has already given the answer. PW is saying 290.

[00:42:58]We have break is saying 290.

[00:43:08]Pushag is also saying 290. Yuku is saying 290. Okay. So this was easy. I'm not going to take that much of time for this one. We can use angles and property of the coordinator. This is 95 105. This missing angle is going to be of 70° because all of the interior angle of the cyclic quadilator are of 360°. Now here also I can see this is forming a complete angle. X + 70 is going to be 360. Therefore, the value of x is going to be 290°.

[00:43:38]290° is the correct answer. Anonymous, your answer is also correct.

[00:43:44]User 3895, your answer is correct. H2O, your answer is also correct. So, we'll have the next one. Let's have the next one. Just give me a minute.

[00:44:00]Just a minute. Let's have this.

[00:44:05]We need to solve for the sum of all the pink angles here.

[00:44:10]Ashu, your answer is correct. 290 is the right answer. Here we need to solve for the sum of all the pink angles. Keep that in mind that the given polygon is a regular polygon and all of the polygons whatever the polygons you are seeing be it a triangle or an on all of them are regular. So the polygons are regular and you need to solve for the sum of all the pink angles. Please be quick with this one. Let's see how many you can do with this.

[00:45:55]Okay, this time we have a new user.

[00:45:59]Philip is saying 900.

[00:46:05]Anyone else guys?

[00:46:10]Kushagra is also saying 900. Yoga is saying 900°.

[00:46:17]Okay, three users with the same answer saying 900. Let's just wait for a few more participant and then I'm going to get the explanation soon.

[00:46:25]We'll see if it is correct or not.

[00:46:36]Inelectable uh Mr. I had given the information already that all of the polygons whatever the polygons whatever the triangles or be it an ongon also they are regular polygons I have mentioned that already they saying 900 yes 900 Eddie Barber is saying 900 let's see guys if how it's going to be like 900 uh as I already mentioned that this is a regular polygon and first of all if I'm going to look at the number of sides here how many sides are there 1 2 3 4 5 6 7 8 9 there are nine sides so it's a nongon and every single angle of a nonagon is of 140° now let's consider every uh angle let's consider this point here right so this as every single angle is of 140° this is also going to be of 140° edib Assuming the triangles are equal. I already mentioned that they are regular polygon which means it is an equilater triangle. They are all are equalated triangle. Okay. So this is 140. And if these are also regular which mean the side of all of the triangles are equal.

[00:47:54]So they are also going to be equal triangle and every corner angle of an equilater triangle is of 60°. So this is 60 this is also 60. Now considering this point and applying the corner complete angle property here sum of all the angle is going to be of 360° right. So I can solve for this pink angle. Let me just mark it as X. So the value of X is going to be of 100°.

[00:48:17]Now how many total angles are there?

[00:48:21]There are total nine angles and one angle measure 100°. So 100 into 9 will give you 900 as sum of all the pink angles. So 900 is the correct answer.

[00:48:34]Bin your answer is correct.

[00:48:37]My voice is low.

[00:48:40]They worth I'm not audible guys.

[00:48:44]900 is the right answer.

[00:48:48]So common choco your answer is not correct. 840 is incorrect. Eddie Barbway your answer is correct. Dworth your answer is correct. Yuko your answer is correct. Pushre and Dip. So Dilip, Pushadri, Yuko, Draat, Eddie Baba and uh Bren, you guys are correct. 900 is the right answer for this one. 360 is incorrect. 7 900 is the correct answer. I already had given the explanation. It's not 720.

[00:49:22]It's 360. It's not 360.

[00:49:26]So you can check the logic. 900 is the final answer.

[00:49:33]So that's all for today guys. This was the last question for today. I'll see you tomorrow at the same timings. Till then take care. Bye-bye. Have a good night.

[00:50:10]This was the last question. Mr. Nigle, every corner, every exterior angle of the polygon some of the all the exterior angle of a polygon is definitely 360.

[00:50:22]But the this uh these are not the exterior angle. If you can see exterior angle is something which is going to correspond along the side of the polygon. So this is going to be an exterior angle right. But here this is not the case.

[00:50:38]So you are going to solve for these angles and find this angle first of all using the complete angle property and this angle was 100°. I already mentioned that I had already shown the explanation. So 900 is the correct answer for this one and I hope it is clear to everyone. Most of the user has already given the correct answers. 900 is the correct one. You can take the screenshot. Think about it. Your reasoning is correct. But here pink angles are not the exterior angle.

[00:51:11]Read about it. All right guys, I'll see you tomorrow at the same timing. Till then take care. Bye-bye. Have a good night. Bye. Will. Thank you.