.please write it in a sum way not in words

• The tick marks on $AD$ indicate $AB = BC = CD$.
• The tick marks on $AE$ indicate $AF = k$ (one tick) and $FG = GE = m$ (two ticks).
• For the problem to be solvable with the given angle relationships, we must assume that the lines $BF$, $CG$, and $DE$ are parallel. This implies that the segments on the transversals are proportional, which means $AB=BC=CD$ and $AF=FG=GE$.
• Therefore, we assume $AB=BC=CD=AF=FG=GE$. Let this common length be $L$.
• Given angles: $\angle AFG = 5y$, $\angle ADE = 2y$, $\angle AED = x$.

If $BF \parallel CG \parallel DE$, then $\triangle ABF \sim \triangle ACG \sim \triangle ADE$.
From similarity, corresponding angles are equal:

• $\angle ABF = \angle ACG = \angle ADE$
• $\angle AFB = \angle AGC = \angle AED$

Given $\angle ADE = 2y$, we have:

Given $\angle AED = x$, we have:

Since we assumed $AF=FG=L$, $\triangle AFG$ is an isosceles triangle with base $AG$.
The angles in $\triangle AFG$ are $\angle FAG$ (which is $\angle A$), $\angle AFG = 5y$, and $\angle FGA$.
We know $\angle FGA = \angle AGC = x$.
The sum of angles in $\triangle AFG$ is $180^\circ$:

The angles in $\triangle ADE$ are $\angle A$, $\angle ADE = 2y$, and $\angle AED = x$.
The sum of angles in $\triangle ADE$ is $180^\circ$:

Subtract equation (2) from equation (1):

A value of $y=0$ is impossible for an angle in a triangle. This indicates that the given angle labels in the diagram are inconsistent with the geometric properties of parallel lines and similar triangles, even under the assumption that $BF \parallel CG \parallel DE$. Therefore, a numerical solution for $x$ and $y$ cannot be determined from the given information.