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Hardest Easy Math Problem
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hints ascending in their usefulness from top(very vague) to bottom(discreet):
1 SPOILER the sum of all three angles in any triangle is always 180°!
2 SPOILER calculate some angles! ;)
3 SPOILER usually in geometry the points of any shape are counted incremental A, B, C, ... always one next letter per increment.
4 SPOILER one letter has been skipped! For a reason...
5 SPOILER point D is missing and you have to create it to solve the problem!
6 SPOILER between which letters is D in the alphabet?
7 SPOILER create point D on the line between C and E
8 SPOILER draw the line DB
9 SPOILER consider the triangle DBC
10 SPOILER D is not fix yet. Try to pick a place for D which is for your advantage
11 SPOILER put D where DBC is a isosceles triangle (a triangle where two sides are of equal length and therefore has two equal angles)
12 SPOILER angle BCD is 80°. Which angle do you need to set for CBD for CDB to equal BCD=80°?
13 SPOILER set CBD=20° so that CDB=180°80°20°=80°=BCD. triangle BCD is now a isosceles triangle. lines BC and BD have the same length! BC=BD
14 SPOILER try to find more isosceles triangles.
15 SPOILER An isosceles triangle is a triangle where two sides are of equal length and therefore must have two equal angles. But vice versa it's also true that it is a triangle which has two equal angles and therefore must have two sides of equal length!
16 SPOILER calculate the angle BFC
17 SPOILER angle BFC=50°
18 SPOILER since angle BFC=50° and angle BCF=50°, triangle BCF is an isosceles triangle! sides BC=BF
19 SPOILER try to find even more isosceles triangles.
20 SPOILER you need to create a line
21 SPOILER draw the line DF
22 SPOILER calculate angles DBF BDF and BFD
23 SPOILER All angles in triangle BDF are 60°. triangle BDF is an equilateral triangle! All sides of this triangle have the same length! BD=BF=DF (=BC)
24 SPOILER analyse triangle BDE
25 SPOILER triangle BDE is also an isosceles triangle! DB=DE (=BC=BF=DF)
26 SPOILER now analyse triangle DEF
27 SPOILER since DE=DF, triangle DEF is also an isosceles triangle.
28 SPOILER angle DFE = angle DEF
29 SPOILER DFE=70°=DEF
30 SPOILER x=DEF40°=30°

Langley's Adventitious Angles is a mathematical problem posed by Edward Mann Langley in the journal The Mathematical Gazette in 1922.
Chinese paper describing geometric solution of anonymous "Ms. aerile_re" in 2015 translated to English
"This work solves the first of the three unsolved problems listed by Rigby in his 1978 paper [of the journal The Mathematical Gazette]"Last edited by Linkblade; 03272020, 12:03 PM.
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