Question

You may use only elementary geometry, solve for x.

Answer 1

You may use only elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use trigonomery, such as sines and cosines, the law of sines, the law of cosines, etc.

Answer 2

just can't quite get the little triangle's angle at D...

Answer 3

dizzying :)
It needs the vertical angle theorem (that where a pair of vertical angles is congruent)
and the fact that the interior angles of a triangle add up to 180 degrees.

We can use those, right?

Answer 4

verticle... whatsit?

Answer 5

got the interior 180 down

Answer 6

never mind... rethinking... :D

Answer 7

k i got C is 20, the lower of the angles in x triangle is 50... now i'm stuck...

Answer 8

lower angle at D is 40

Answer 9

lower angle at E is 30

Answer 10

can i do something with triangle ACE to work it out... somehow... maybe...?

Answer 11

anyone got anything yet...? coz i'm stuck ;)

Answer 12

Something about ACE

Answer 13

bothers me

Answer 14

simultaneous equations...?
a Taylor expansion...?
Laplace transform...?

Answer 15

hahah, bothers me

Answer 16

From the angle sum of a triangle, it follows that
A + C + E = 180
(A,C,E from the context of triangle ACE)

Answer 17

So...
10 + 20 + E = 180

Answer 18

right?

Answer 19

yep, but we know its 150 from the lower angle of E being 30...

Answer 20

x = 20

Answer 21

@ganeshie8 how?

Answer 22

nvm wrong calc

Answer 23

What if I told you that there are at least two possible solutions for x....?

Answer 24

go on...

Answer 25

i'd tell u im intrigued

Answer 26

First, I need to draw.

Answer 27

We can come up with this....

Answer 28

Furthermore...
These we know to be true, so far, right?

Answer 29

yep, perfect
plus a medal for awesome artistry ;P

Answer 30

Now, let's arbitrarily assign a value to x.
(if it were the wrong value, we should get some major inconsistencies)