Angle level 8 question? Got deleted so i am re posting it

Level 8 maths angle question number three?
In the diagram, DE is parallel to BC
and FD is parallel to CA.
Three angles of 6xº and 4xº and 7xº
are shown. Angle EFC is twice angle
DBF.
Calculate the sizes of the angles of
triangle DEF
http://www.m4ths.com/web_documents/ex__s_in_ks3_levels_7-8.pdf

Isn't it question 4 on that file?? xD hehe

KEY: (( A(DBF) = Angle DBF ))
Before you read, label all angles that you can using the rules you have learnt.
Plus, draw out as you read ;)

You are told:
A(EFC) = 2 x A(DBF)
Therefore:
4x = 2 x A(DBF)
2x = A(DBF)

Using angles in Triangle 'BDF::
A(DBF) + 6x + 7x = 180
Therefore:
A(DBF) = 180 - 13x

Because 2x = A(DBF)

You get:
2x = 180 - 13x
15x = 180
x = 12

NOW JUST SOLVE WITH WHAT YOU KNOW
A(DFE) + 6x + 4x = 180
A(DFE) = 180 - 10x
A(DFE) = 180 - 10(12)
A(DFE) = 60deg

A(DEF) + A(AED) + A(CEF) = 180
A(DEF) + 6x + 60 = 180
A(DEF) = 120 - 6(12)
A(DEF) = 48deg

A(EDF) + A(DFE) + A(DEF) = 180
A(EDF) + 60 + 48 = 180
A(EDF) = 180 - 48 - 60
A(EDF) = 72

Hope this help.. coz damn it was long to write... :)

Ok this is extremely hard to explain with just text, because of all the letters but I will try. I encourage you to try and work what I am saying out on a piece of paper so its more clear.

1) (Angle) DEF has a measure of 4x (alternate interior angles)
2) EDF has a measure of 6x (alternate interior angles)
3) Thus, DFE has a measure of 180-6x-4x or just 180-10x

Now that you have all your interior angles in terms of x, you have to find a way to solve for x

1) Angle DBF= 1/2 EFC = 2x
2) Thus BDF= 180-8x
3) BDF also = 7x, because Triangle DBF and Triangle ADE are similar.
4) Thus we find that 7x=180-8x, solve for x and you get x=180/15, which is 12
5) Plug 12 back into the original formula's for the angles in triangle DEF
6) 4*12= 48, 6*12= 72, 180-120= 60
7) Check the answer by adding 48+72+60, to make sure it equals 180 and is a valid triangle.

THATS IT, Again that's a lot to take in at once so if you truly want to understand this problem, go back and work through each step. Feel free to message me if you are still confused.

Do you really expect anyone to trawl through about 100 pages of crap to find what you are referring to? That's probably why it got deleted. No-one could be bothered. If you make it so difficult to find the question, it'll probably get deleted again. Help is one thing; but you don't help yourself by expecting anyone to waste their time searching for the question. Better things to do.

P73
Q4

For anyone who knows