Let ABC be a triangle where AB = BC = AC.
From A, draw a line that intersects BC at a point D.
From the AD segment, draw a 20 degrees line that intersects AB at a point E. Determine the angle DEC.
This is not an easy problem.
Hint: Try to see invisible things.
Good luck. And consider yourself a genius if you resolve it in less than 30 minutes. Don't feel bad about yourself if you don't resolve it at all.

80° is my try after 2 mins

Originally posted by smaia
Let ABC be a triangle where AB = BC = AC.
From A, draw a line that intersects BC at a point D.
From the AD segment, draw a 20 degrees line that intersects AB at a point E. Determine the angle DEC.
This is not an easy problem.
Hint: Try to see invisible things.
Good luck. And consider yourself a genius if you resolve it in less than 30 minutes. Don't feel bad about yourself if you don't resolve it at all.

let me clarify a bit -
Going clockwise, mark points A, B, C such that AB = BC = CA. (i.e , the triangle is equilateral).
1- take A: The side opposed to A is BC. Draw a perpendicular line from A to BC. This line will intersect BC at point D - Note that because the line is perpendicular to BC => BD = DC.

2- Now, take the segment AD. Draw a 20 degrees segment (having AD as reference) that starts at D and intersects AB at a point E, i.e. the angle ADE is 20 degrees.

3- Link E to C.
4- Determine angle DEC

I hope this helps

It is not 80. Take at least 15 minutes and see what you get.

Originally posted by smaia
let me clarify a bit -
Going clockwise, mark points A, B, C such that AB = BC = CA. (i.e , the triangle is equilateral).
1- take A: The side opposed to A is BC. Draw a perpendicular line from A to BC. This line will intersect BC at point D - Note that because the line is perpendicular to BC => BD = DC.

2- Now, take the segment AD. Draw a 20 degrees segme ...[text shortened]... .e. the angle ADE is 20 degrees.

3- Link E to C.
4- Determine angle DEC

I hope this helps

Originally posted by wolfgang59
I understand the question now! Whether that helps or not .....

Originally posted by wolfgang59
I understand the question now! Whether that helps or not .....

21º?

Edit: 32º

Originally posted by Green Paladin
21º?

Edit: 32º

Originally posted by wolfgang59
Good Puzzle. Cant do it!

DEC = 32.55º

I gave the equilateral triangle sides with 9 units.

AD = 7.8
AE = 3.48
EC = 7.86
ACE = 22.55º
ECD = 37.45º

First I worked out AD. With AD you can solve AE. With AE you can work out EC. With EC you can work out angle ACE.

Angle ECD = 37.45º (60 - 22.5). Angle EDC (110) plus angle ECD (37.45) = 147.45º. The sum of the angles of a triangle = 180º -147.45º = 32.55º.

Is this correct?

Originally posted by Green Paladin
DEC = 32.55º

I gave the equilateral triangle sides with 9 units.

AD = 7.8
AE = 3.48
EC = 7.86
ACE = 22.55º
ECD = 37.45º

First I worked out AD. With AD you can solve AE. With AE you can work out EC. With EC you can work out angle ACE.

Angle ECD = 37.45º (60 - 22.5). Angle EDC (110) plus angle ECD (37.45) = 147.45º. The sum of the angles of a triangle = 180º -147.45º = 32.55º.

Is this correct?

Originally posted by smaia
Nice try, but the answer is not 32.55
If you want to follow your approach, you need to set AB = x where x is any real number.
Good luck.

Originally posted by Green Paladin
Ok, I've checked my numbers. Final attempt (with no rounding off) - 32.725229402º