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.

$\angle HOF$

Short answer

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

Step-by-step solution

Step 1. Observe the given statement and figure.

The provided angle consists of two angles which are$\angle GOF$ and$\angle HOG$ where the$\angle GOF$ is present in vertical opposite side of$\angle BOC$.

Step 2. Make an equation.

Using the observation make an equation.

$\angle HOF=\angle GOF+\angle HOG$

Step 3. Determine the required value.

As the $\angle GOF$is present in the vertical opposite side of $\angle BOC$which means that $\angle GOF$can be replaced with $\angle BOC$by substituting the value of $\angle BOC$and $\angle HOG$into the obtained equation, determine the value of the provided angle.

$\angle HOF=\left(x+y\right)°$