Question

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

$m\angle ABD=3x-12$, $m\angle DBE=2x+2$, $m\angle EBF=2x+8$

Short answer

The number 20 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 90° 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.

$$\begin{gathered} 3x+2x+2-12=90° \\ 5x-10=90° \\ 5x=100° \\ x=\frac{100}{5} \\ x=20° \end{gathered}$$