Question

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

$m\angle ABD=2x-15$, $m\angle DBE=x$.

Short answer

The number 35 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 $\angle ABE$ that represent themselves 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.

$\angle ABD+\angle DBE=90°$

Step 3. Determine the value of x

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

$$\begin{gathered} 2x-15+x=90° \\ 3x-15=90° \\ 3x=105° \\ x=\frac{105}{3} \\ x=35° \end{gathered}$$