Question

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

$m\angle DBE=3x$,$m\angle EBF=4x-1$

Short answer

The number 13 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 given angles are having the measurement of 90° if they are added because these angles are parts of ∠DBF that represent itself as a right angle.

Step 2. Make an equation by using the observation.

As the 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.

$\angle DBE+\angle DBF=90°$

Step 3. Determine the value of x.

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

$$\begin{gathered} 3x+4x-1=90° \\ 7x-1=90° \\ 7x=91° \\ x=\frac{91}{1} \\ x=13° \end{gathered}$$