Triangle Nightmare

Originally posted by Jirakon
De ja vu... I remember a puzzle like this one on this board from a long time ago. It was an equilateral triangle with an altitude and two other lines drawn. One angle was given (20 degrees), and the angle to solve for was ~32.54 degrees (I can't believe I still remember that number). I solved it with trig, but it took a while to convince some of the posters ...[text shortened]... (several people kept thinking it was 30 degrees). Does anyone remember what I'm talking about?

I remember, ....I tried to find it, no sucess.

Originally posted by sven1000
Assuming A and C are points on the base, so that angle ABC=20 deg.

Point D is where the 40 deg line above the base AC intersects side BC. Point E is where the 30 deg line above the base AC intersects side AB. Point F is where the lines AD and CE intersect in the mid-region of the triangle ABC.

we know that FAC is 40 degrees and FCA is 30 degrees (both by definition) - therefore AFC must be 110

if AFC is 110, then adjacent angle AFE must be 70 -- and opposite angle EFD is 110

EAF is 40 degrees (half of the original 80 degrees), so AEF is 180-(AFE+EAF) or 70

since AEF is 70, adjacent angle BEF is 110

since AFE is 70, opposite angle CFD must also be 70; FCD is 50 degrees (the original 80 degrees minus 30) -- so FDC is 60 degrees

if FDC is 60, then adjacent angle ADB is 120

finally - as a check -- the quadrilateral made up of angles BEF, EFD, FDB, and DBE = 110 + 110 +120 + 20 = 360

all of this would be MUCH easier to explain if a diagram could be posted as an illustration

Originally posted by Melanerpes
we know that FAC is 40 degrees and FCA is 30 degrees (both by definition) - therefore AFC must be 110

if AFC is 110, then adjacent angle AFE must be 70 -- and opposite angle EFD is 110

EAF is 40 degrees (half of the original 80 degrees), so AEF is 180-(AFE+EAF) or 70

since AEF is 70, adjacent angle BEF is 110

since AFE is 70, opposite angle CF ...[text shortened]... 0

all of this would be MUCH easier to explain if a diagram could be posted as an illustration

FDE? FED? BED? BDE?

Originally posted by Palynka
FDE? FED? BED? BDE?

I see - you have to connect D & E -- I misread the original question 😛 -- it seemed too easy