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, $\frac{AD}{DC} = \frac{AB}{BC}$. Here, $AD = 2$, $DC = x$, $AB = 7$, and $BC = 8$. So we have the proportion $\frac{2}{x}=\frac{7}{8}$.

Step2: Solve for \(x\)

Cross - multiply the proportion $\frac{2}{x}=\frac{7}{8}$ to get $7x=2\times8$. Then $7x = 16$. Divide both sides by 7: $x=\frac{16}{7}\approx2.3$ (rounded to the nearest tenth).

Answer:

\(2.3\)