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.

$\angle COA$

Short answer

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

Step-by-step solution

Step 1. Observe the given statement and figure.

The provided angle consists of two angles which are ∠BOC and ∠AOB where the ∠AOB represents itself as a right angle.

Step 2. Make an equation.

Using the observation make an equation.

$\angle COA=\angle BOC+\angle AOB$

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 ∠AOB is formed by the provided perpendicular lines so by substituting the value of ∠BOC and ∠AOB into the obtained equation, determine the value of the provided angle.

$\begin{array}{c}\angle COA=\left(x+90\right)°\\ =\left(90+x\right)°\end{array}$