mingkkoo1
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.
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NotTim
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Koala Bird, MEet Pengu.
mingkkoo1
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NotTim
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Koala Bird left.
mingkkoo1
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WHat?
mingkkoo1
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uh..... DONT LEAVE????
NotTim
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Err. Start off nice an simple.
mingkkoo1
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Koala Bird!!
NotTim
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The bottom triangle, a to b; you can find out the last angle knowing that the total angle fo a triangle is 180.
mingkkoo1
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k
mingkkoo1
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mingkkoo1
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NotTim
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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.
mingkkoo1
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mingkkoo1
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mingkkoo1
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NotTim
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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)
mingkkoo1
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k
NotTim
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KOALA BIRD IS BACK
NotTim
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Er, whatever I'm thinking of, may be overcomplicating the question...
moneybird
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@Not Tim You got the answer?
NotTim
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Noo....
mingkkoo1
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nooooo
NotTim
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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.
NotTim
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But done I would only get 1 angle for Triangle CDE
NotTim
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Unless.
NotTim
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Pengu, did yo uget all the angles within the triangle that reaches---WAIT. NO
NotTim
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That wouldn't work, as I would need the angles with CDE...
NotTim
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Sorry. I reached the end of my useful line.
moneybird
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I find that triangle CDB is an isosceles triangle
JamesJ
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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.
NotTim
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Imma leave. Sniff.
babystar16
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hey mingkkool1.