Question

solve for x. figures are not necessarily drawn to scale.

Explanation:

Step1: Use the similarity of triangles

Since \(\angle DCE=\angle BCA\) (vertical angles) and \(\angle E=\angle B\) (given by the arrow marks indicating parallel lines or similar angles), \(\triangle DCE\sim\triangle BCA\).
For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{DC}{BC}=\frac{DE}{AB}\).

Step2: Substitute the known values

We know \(DC = 3.6\), \(BC=9\), and \(AB = 6\). Let \(DE=x\).
Substituting into the proportion \(\frac{3.6}{9}=\frac{x}{6}\).
Cross - multiply: \(9x=3.6\times6\).

Step3: Solve for \(x\)

First, calculate \(3.6\times6 = 21.6\). Then, \(x=\frac{21.6}{9}\).
\(x = 2.4\).

Answer:

\(2.4\)