using the given diagram, solve for x.\nx = (simplify your answer.)

Answer

Explanation:

Step1: Apply the angle - bisector theorem

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, $\frac{10}{x}=\frac{6}{3}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{10}{x}=\frac{6}{3}$ gives $6x = 10\times3$.

Step3: Simplify the right - hand side

$10\times3=30$, so the equation becomes $6x = 30$.

Step4: Solve for x

Dividing both sides of the equation $6x = 30$ by 6, we get $x=\frac{30}{6}=5$.