Question

1. solve for x. 11.5 11.75 11.25 11

Explanation:

Step1: Apply the angle - bisector theorem

The angle - bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides. So, we have the proportion $\frac{9}{x}=\frac{10}{12.5}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{9}{x}=\frac{10}{12.5}$ gives us $10x = 9\times12.5$.

Step3: Solve for x

First, calculate $9\times12.5 = 112.5$. Then, $x=\frac{112.5}{10}=11.25$.

Answer:

$11.25$