Hi guys, I'm doing this to help the weak one

If you have any problems with PMR, kindly post here or email me at HozhunVylox at gmail.com

If Maths subject or science need pictures to solve, do not hesitate to upload it, I'll help whoever has problem with it.



Sincerely,
ChuckyHuntsYou

Don't hunt me, Chakie. But can you provide a step-by-step workout to determine angle x as shown below, using ONLY elementary geometry, such as the sum of internal angles and other basic properties of a triangle. I remember my math teacher said trigonometry, the law of sines, and the law of cosines are not allowed. And it is not a trick question.

I'll try my best
And trigonometry won't work in this question at form 3 level.

This post has been edited by ChuckyHuntsYou: Aug 30 2013, 01:50 PM

I suppose the answer is
x = 20° ?

I, frankly do not know the true answer, and I'm not testing you. It is just a look-so-easy geometry problem. I must humbly tell you that I have also worked on it for many hours since yesterday to determine angle x using only elementary geometry. Perhaps, it is time to invite Krevaki, p3nguin, studyboy, & TSOM to unleash the Wisdom of Crowds.

Hi Flame Haze, Intermission, kingkingyyk, maximR

If you have some time, please drop by this thread because I want to borrow your Brilliance to find the angle x!

Thanks for bringing this to my notice. It's an interesting question, and I must admit I'm not any closer to the answer after 1 hour of brain-squeezing. I'll give it another try tomorrow.

At first, I was thinking there must be some kind of geometrical properties either so new or unknown to me. But after draining all my grey matter, I finally discovered the following relationship which can be mathematically proven. However, I'm not sure whether I have just rediscovered the work of other scholar, or the theorem has been repeatedly appeared in numerous publications in the past. Anyhow, by applying the following theorem, the angle x can be determined in seconds. Perhaps, you could verify this theorem too. Also thanks ChuckyHuntsYou for provoking me!



The above theorem shall be read in conjunction with the Triangle Problem 1 figure.
Some wordings may need to be refined or rephrased in future for the sake of clarity.
Point 'O' (not shown in figure) is the intersection between Line AE and Line BD.

This post has been edited by Critical_Fallacy: Aug 31 2013, 05:57 AM

don't tell me this is PMR question? it just too hard.... damn i have to admit that i am proficient in math but still i can't solve it after 2 hours... shall be continue doing after wake up ..

and what is fallacy's theorem?? can't find by googling ..... are you providing the correct name?

answer is 20 degree. i drew the figure ..

This post has been edited by trewq: Aug 31 2013, 06:20 AM

I believe that this solve the question using only elementary geometry(in pmr level).
I draw the triangle out and measure the length of each side and backtrack the solution from there.
Well, it took me a whole night for this...

This question should only be appearing in objective. Should I be the candidate, I will just draw it out.
It just take only a minute or two to obtain the answer by drawing.
This is a very hard problem(which i think that even most of university student can't solve it).
Please do inform me if there is any mistake. Looking forward if there is other simple method.
Well, as far as I am concern, there is no way of jumping into conclusion that ∠DBE or ∠DBC = ∠DEA = 20 degree.

Good luck in understanding the solution. I hope that it is clear enough to be understand.

Solution starts here:
Upon googling, i found out that the above question is extended from a question known as Langley's problem. You can refer the solution to Langley's problem below, which i will not be further explaining.

http://agutie.homestead.com/files/LangleyProblem.html

Therefore, to solve the problem, we need to construct additional line AF where F intersect line CB such that ∠FAB = 50 degree and connect point F to point D forming line DF which in the end results in solving Langley's problem.
The diagram is shown below.



Maybe you would like to continue from here.
I have hide the solution in the spoiler below.



This post has been edited by macamtakada: Aug 31 2013, 08:19 AM

Anyone can tell me how do I upload a picture ? It says I'm against no do my homework
New here~

Take a picture with your phone then upload it to imageshack.us then share the link here

--------------------------------------------------------------
Yes the answer is 20 degrees
I'm the one that solved it first

You need to make another congruent triangle to solve it.

http://imgur.com/9eVAq06
http://imgur.com/WQ296hF
http://imgur.com/YgEERZU
http://imgur.com/IMof7Ay

Here is it

Q1

L = e(R+4) / R
LR = eR + 4e
(L-e)R = 4e
R = 4e / (L - e)

Q2

(h^2)^m(h^3) = h^4
h^(2m + 3) = h^4
2m + 3 = 4
2m = 1
m = 1/2

Q3

7 - 2x < 4
2x > 3
x > 3/2

x - 3 <= 2
x <= 5

x: x <= 5 and x > 3/2

Q4

(a) 6m3r2 + 12m2r = 6m2r(mr + 2)

(b) f2 - 4f - 5 = (f - 5)(f + 1)

Both of you have my utmost respect.

The moment I labeled all angles that I could possibly know using the fact that sum of angles of a triangle is 180, I know some construction is definitely needed in order to solve this problem. So what I draw a scaled diagram and obtain the answer instead. But the question remains, how did you know what congruent triangle to construct?

3 years ago when I was form 3 geometry was my favorite topic in mathematics but till this day it remains the only topic that is not expanded in my upper secondary education even when I am taking further mathematics. Algebra evolved into something unimaginably complicated that I could not have recognized back then, but I haven't learn much more new geometry except coordinate geometry ever since.

Perhaps it boils down to experience and intuition. Anyway, try if that you can prove that △CED is similar to △EFB where F is the intersection point of BD and AE. If you can prove that, then it solves the question.