Question

the diagram is not drawn to scale. 20 2x - 8 33. find the value of x. 14 10 9 11

Explanation:

Step1: Identify mid - segment theorem

The line segment with length $2x - 8$ is a mid - segment of the triangle. The mid - segment of a triangle is half the length of the parallel side. Here, the parallel side has length 20.

Step2: Set up the equation

According to the mid - segment theorem, $2x-8=\frac{20}{2}$.

Step3: Simplify the right - hand side

$\frac{20}{2}=10$, so the equation becomes $2x - 8=10$.

Step4: Solve for x

Add 8 to both sides of the equation: $2x=10 + 8$, so $2x=18$. Then divide both sides by 2: $x=\frac{18}{2}=9$.

Answer:

9