Only 2% of people can solve this. Are you a genius? - Free Educational videos for Students in K-12

Only 2% of people can solve this. Are you a genius? - By tecmath

Transcript


00:0-1	Good day and welcome to the Tech mouth channel Problem
00:02	I have for you today is we have a triangle
00:04	. In fact , we have two triangles . We
00:05	have a little triangle sitting inside a bigger triangle .
00:09	We know the following . We know this little angle
00:11	here is 20 degrees . We know this angle here
00:14	is 80 degrees . We also know that this length
00:17	here is equal to this length here . What we're
00:20	trying to find and this is your challenge is can
00:23	you find this unknown angle here ? Using only basic
00:27	geometry ? You're not allowed to use trigonometry on this
00:29	one ? You have to use basic geometry . So
00:32	can you go about and do that Anyway , pause
00:34	the video and see how you go and I'll come
00:37	back with the answer . Okay , so time's up
00:53	. Did you manage to solve it ? I'll tell
00:54	you what , I'm going to go through how to
00:55	work out this answer right now . So the first
00:58	we're going to do is I'm going to label the
01:00	different corners of this triangle just to help us with
01:04	the explanation . So we have this corner here ,
01:06	I'm going to call a this corner here . I'm
01:08	going to call be this corner here . I'm going
01:10	to call C . And this part here , I'm
01:13	going to call D where this intersection here occurs .
01:16	So the first we're going to work out to solve
01:18	this is what this angle is down here . We
01:20	know that we have a triangle here and we have
01:23	an angle of 80 and an angle of 20 .
01:26	Now , angle A . B C . That is
01:28	, this angle down here is going to equal 180
01:32	minus these two and also 180 degrees minus 80 degrees
01:38	minus 20 degrees because in the entire of a triangle
01:41	there is 180 degrees , so 180 minus 80 minus
01:46	20 is equal to 80 . So we know this
01:48	angle down here is equal to 80 degrees . So
01:52	what does this tell us if this angle here is
01:55	80 degrees and this angle here is 80 degrees .
01:57	What this means is our triangle is an isosceles triangle
02:01	. This triangle , A , B C . Is
02:05	ice oscillates . That means we have to equal angles
02:08	and on top of that we have to equal length
02:10	here . So we can actually mark these on .
02:12	I'm going to mark these two equal lengths on right
02:15	now . We have this length here and we have
02:17	this length here . The next thing we're going to
02:20	do to solve this problem is we are going to
02:22	draw an equilateral triangle that comes off this line here
02:25	. An equilateral triangle has equal side lengths and equal
02:28	angles . So an equilateral triangle would come out up
02:30	here and it would go down to this park here
02:34	. I'd had a side length here and these side
02:37	length would be the same and this side length here
02:39	would also be the same . Now we can also
02:41	label the angles on our equilateral triangle here . We
02:44	know that this angle up here , I'm going to
02:45	call this E R . P . R . We
02:47	know that this angle is going to be equal to
02:50	60 degrees because 180 divided by three is equal to
02:53	60 . We could work out this little part of
02:56	the angle here because if this entire angle here is
02:59	60 degrees , well 60 take away 20 that would
03:03	tell us that this angle here is 40 degrees .
03:06	The last thing we're left with is this angle here
03:08	, which is also 60 degrees . So the next
03:11	thing we're going to work out is this angle here
03:14	? This angle E . B . C . Okay
03:17	, I'll destroy it in there . Now , what
03:19	do we know about this particular area ? We know
03:22	that A . B . C . Is equal to
03:24	80 degrees . This entire angle here , we also
03:27	know that on our collateral triangle this is equal to
03:31	60 degrees . So this little angle , this E
03:34	B C is going to equal 80 degrees minus 60
03:38	degrees . So a t minus 60 . This is
03:41	going to equal 20 degrees . All right . So
03:45	let's get up to the next step . Now ,
03:47	we're going to draw a line between C and the
03:53	and this gives us a triangle A C . E
03:56	. Now , what do we know about triangle ?
03:58	A . C . E . Well , we know
04:00	it is also an isosceles triangle . What makes me
04:04	say that ? Or we have this line here at
04:08	this lawyer here Of equal length . So straight away
04:11	this tells us we have an isosceles triangle . So
04:14	now what we can do is we can work out
04:16	a few of our unknown angles here , using this
04:19	, what we know is this angle here and we
04:21	work that out well , pretty simply right because we
04:24	know this angle down here is 40°. . A triangle
04:28	in total has 180°, , so we go 180° -40°.
04:34	. And then we divide our result by two ,
04:37	dividing at least two angles here . It will tell
04:40	us how big this angle here is . So 180
04:43	minus 40 is 100 and 40 divided by two .
04:47	This angle is 70 degrees and we've almost solved this
04:51	problem because what we've managed to create is two congruent
04:54	triangles . That is to say two triangles that are
04:57	similar in form . Okay , can you see where
05:00	they are ? Okay , we're going to use information
05:03	from one and transfer it across the other and use
05:05	this to solve our problem . If you have a
05:07	look at the first triangle here , we're going to
05:10	have a look at the B . C . Okay
05:13	, we have this length here and it has a
05:16	20 degree angle and this shorter length here . Okay
05:21	. We have triangle the B . C . Can
05:24	you spot the triangle that it is congruent to maybe
05:27	you did . We have the long length from be
05:29	going across A . We have this 20 degrees and
05:32	then we have this shorter length here . It's going
05:34	to be covered over there . So you might not
05:36	have seen it where it goes off from A two
05:38	D . Okay , so this is B . A
05:41	. D . These two triangles are congruent one another
05:44	there are identical . So we know this little angle
05:48	here . We can find out what it is because
05:50	we know it's the same as this angle here which
05:53	is 80 Plus 70 . So what's 80 plus 70
05:56	, 80 plus 70 is equal to 150° in a
06:02	straight line , there is 100 and 80 degrees .
06:04	So we've got our final angle , our angle that
06:07	we have to solve this is going to be equal
06:08	to 180 degrees minus 150 degrees , which is equal
06:15	to 30 degrees . And that is our answer .
06:18	Our answer is 30 degrees . So how did you
06:22	go ? Did you manage to solve this problem before
06:24	me without using trigonometry ? If you did let us
06:26	know in the comments below and if you like this
06:28	video , please also let us know in the comments
06:30	below and hit the like button and subscribe for more
06:33	problems and our math tips and tricks to come along
06:36	. Anyway , thank you for watching and we'll see
06:38	you next time . Bye .

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