Question

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

Explanation:

Step1: Apply 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, $\frac{CD}{DA} = \frac{BC}{BA}$.
Given $CD = 15$, $DA = 19$, $BA = 20$, and $BC = x$. So, $\frac{15}{19} = \frac{x}{20}$.

Step2: Solve for \( x \)

Cross - multiply to get $19x = 15\times20$.
Calculate $15\times20 = 300$. Then, $x=\frac{300}{19}\approx15.8$.

Answer:

\( 15.8 \)