Question

In the figure $\overleftrightarrow{BF}\perp \overleftrightarrow{AE}$, $m\angle BOC=x$, and $m\angle GOH=y$. Express the measure of the angle in terms of x, y, or both.

$\angle DOE$

Short answer

The required value of the provided angle is$\left(90-\left(x+y\right)\right)°$.

Step-by-step solution

Step 1. Observe the given statement and figure.

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

Step 2. Make an equation.

Using the observation make an equation.

$\angle DOE=\angle BOE-\left(\angle COD+\angle BOC\right)$

Step 3. Determine the required value.

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 $\angle BOE$is formed by the provided perpendicular lines and $\angle COD$is present on the vertical opposite side of$\angle HOG$ which means that $\angle COD$ can be replaced with $\angle HOG$.

$\angle DOE=90-\left(\angle HOG+\angle BOC\right)$

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

$\angle DOE=\left(90-\left(x+y\right)\right)°$