## mingkkoo1 3 years ago 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.

1. NotTim

Koala Bird, MEet Pengu.

2. mingkkoo1

3. NotTim

Koala Bird left.

4. mingkkoo1

WHat?

5. mingkkoo1

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

6. NotTim

Err. Start off nice an simple.

7. mingkkoo1

Koala Bird!!

8. NotTim

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

9. mingkkoo1

k

10. mingkkoo1

k

11. mingkkoo1

k

12. NotTim

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.

13. mingkkoo1

k

14. mingkkoo1

k

15. mingkkoo1

k

16. NotTim

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)

17. mingkkoo1

k

18. NotTim

KOALA BIRD IS BACK

19. NotTim

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

20. moneybird

@Not Tim You got the answer?

21. NotTim

Noo....

22. mingkkoo1

nooooo

23. NotTim

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.

24. NotTim

But done I would only get 1 angle for Triangle CDE

25. NotTim

Unless.

26. NotTim

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

27. NotTim

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

28. NotTim

Sorry. I reached the end of my useful line.

29. moneybird

I find that triangle CDB is an isosceles triangle

30. JamesJ

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.

31. NotTim

Imma leave. Sniff.

32. babystar16

hey mingkkool1.