Question

In the diagram,$\overrightarrow{BE}\perp \overleftrightarrow{AC}$ and $\overrightarrow{BD}\perp \overrightarrow{BF}$. Find the value of x.

$m\angle ABD=6x$, $m\angle DBE=3x+9$, $m\angle EBF=4x+18$, $m\angle FBC=4x$

Short answer

The number 9 represents the required value that is for x.

Step-by-step solution

Step 1. Observe the given statement and figure.

The provided information and figure indicate that the first two given angles are having the measurement of 90д if they are added because these angles are parts of ∠ABE that represent itself as a right angle.

Step 2. Make an equation by using the observation.

As the first two given angles are having a measurement of 90° if they are added so these angles fall in the category of complementary angles. Make an equation that represents these angles.

$\angle ABD+\angle DBE=90°$

Step 3. Determine the value of x

Substitute the provided value of∠ABD and ∠DBE into the obtained equation and solve for x.

$$\begin{gathered} 6x+3x+9=90° \\ 9x+9=90° \\ 9x=81° \\ x=\frac{81}{9} \\ x=9 \end{gathered}$$