A property of two triangles, geometry puzzle

[This is a geometry puzzle, solvable by elementary 8th grade geometry, i.e. no trigonometry etc]

In the figure below (not to scale, forgive the shoddy drawing skills).




$ABC$ is a triangle such that $\angle{BAC} = 60$ and $\angle{ABC} = 25$.

$DEF$ is an isosceles triangle, such that $\angle{EDF} = \angle{EFD}$, and $\angle{DEF} = 10$

(all angles are in degrees).

We also have that $|BC| = |DE|$ ($|XY|$ = length of the segment $XY$)

Show that $2|AC| + |DF| = |AB|$

[Solution]