Question

11
x =
2x + 14
18
9
30

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, $\frac{18}{2x + 14}=\frac{9}{30 - 9}$.

Step2: Simplify the right - hand side

First, calculate $30 - 9 = 21$. So the equation becomes $\frac{18}{2x + 14}=\frac{9}{21}$.

Step3: Cross - multiply

Cross - multiplying gives us $18\times21=9\times(2x + 14)$.

Step4: Simplify both sides

Calculate $18\times21 = 378$ and $9\times(2x + 14)=18x+126$. So the equation is $378 = 18x+126$.

Step5: Solve for x

Subtract 126 from both sides: $378-126 = 18x$, which simplifies to $252 = 18x$. Then divide both sides by 18: $x=\frac{252}{18}=14$.

Answer:

14