91Ó°ÊÓ

The provided angle is a part of $∠BOE$which represents itself as a right angle. This angle also consist of two more angles which are $∠BOE$and $∠COD$which means that the value of provided angle can be determined by subtracting the addition of angles $∠BOE$ and $∠COD$ from $∠BOE$.

Using the observation make an equation.

$∠DOE=∠BOE−\left(∠COD+∠BOC\right)$

Use the definition of perpendicular lines that is the relation between two lines is perpendicular when the measurement of angles formed by those lines is equal to 90°. The $∠BOE$is formed by the provided perpendicular lines and $∠COD$is present on the vertical opposite side of$∠HOG$ which means that $∠COD$ can be replaced with $∠HOG$.

$∠DOE=90−\left(∠HOG+∠BOC\right)$

So, by substituting the value of $∠BOE$, $∠HOG$and $∠BOC$into the obtained equation, determine the value of the provided angle.

$∠DOE=\left(90−\left(x+y\right)\right)°$