Originally posted by JirakonI remember, ....I tried to find it, no sucess.
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?
3 edits
Originally posted by sven1000we know that FAC is 40 degrees and FCA is 30 degrees (both by definition) - therefore AFC must be 110
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.
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 MelanerpesFDE? FED? BED? BDE?
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