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.

$\angle COH$

Short answer

The required value of provided angle is$\left(180-y\right)°$.

Step-by-step solution

Step 1. Observe the given statement and figure.

The provided angle consists of two angles which are $\angle BOC$and $\angle HOB$where the $\angle HOB$is also a mixture of $\angle AOB$and $\angle HOA$in which $\angle AOB$represents itself as a right angle and $\angle HOA$is equal to $180°-\left(90°+x+y\right)$ becauseGC represents a straight line.

Step 2. Make an equation.

Using the observation make an equation.

$\angle COH=\angle BOC+\angle HOB$

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

$$\begin{gathered} \angle COH=x+90+\left(180-\left(90+x+y\right)\right) \\ =x+90+\left(90-\left(x+y\right)\right) \\ =\left(180-y\right)° \end{gathered}$$