Question

Using only elementary geometry, determine angle x. Provide a step-by-step proof.

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. There is a review of elementary geometry below.

This is the hardest problem I have ever seen that is, in a sense, easy. It really can be done using only elementary geometry. This is not a trick question.

Answer 1

Koala Bird, MEet Pengu.

Answer 2

Koala Bird left.

Answer 3

WHat?

Answer 4

uh..... DONT LEAVE????

Answer 5

Err. Start off nice an simple.

Answer 6

Koala Bird!!

Answer 7

The bottom triangle, a to b; you can find out the last angle knowing that the total angle fo a triangle is 180.

Answer 8

k

Answer 9

k

Answer 10

k

Answer 11

You can use that new angle to find out the angle that is on the other side of it, knowing that the total angle is also 180.

Answer 12

k

Answer 13

k

Answer 14

k

Answer 15

With that, you can use the new angle you got to find the angle beside it, in triangle DE (the small triangle for which you are seeking)

Answer 16

k

Answer 17

KOALA BIRD IS BACK

Answer 18

Er, whatever I'm thinking of, may be overcomplicating the question...

Answer 19

@Not Tim You got the answer?

Answer 20

Noo....

Answer 21

nooooo

Answer 22

I was thinking: USe all major angles to find the last major angle, and then use the angle collected previously in Triangle DA for the angle. And then Find the angle for Triangle EB.

-In summary, find all angles.

Answer 23

But done I would only get 1 angle for Triangle CDE

Answer 24

Unless.

Answer 25

Pengu, did yo uget all the angles within the triangle that reaches---WAIT. NO

Answer 26

That wouldn't work, as I would need the angles with CDE...

Answer 27

Sorry. I reached the end of my useful line.

Answer 28

I find that triangle CDB is an isosceles triangle

Answer 29

Call the point where the lines AE and DB intersect F.

Then the angle AFB = 180 - (70 + 60) = 50
=> the angle DFA = 130
=> ADF = 40

The angle DCE = 180 - (80 + 80) = 20
=> CEA = 150

That should get you started.

Answer 30

Imma leave. Sniff.

Answer 31

hey mingkkool1.