Question

segment bd bisects \\( \angle abc \\). solve for \\( x \\). round to the nearest tenth, if necessary. (image not necessarily to scale.)

Explanation:

Step1: Apply the Angle Bisector Theorem

The Angle Bisector Theorem states that if a bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. So, \(\frac{CD}{DA}=\frac{BC}{BA}\).
Substituting the given values: \(\frac{11}{14}=\frac{x}{20}\).

Step2: Solve for \(x\)

Cross - multiply: \(14x = 11\times20\).
\(14x=220\).
Then \(x=\frac{220}{14}\approx15.7\).

Answer:

\(x = 15.7\)