Question

find the value of x

Explanation:

Step1: Use the property of the mid - segment of a triangle

In a triangle, if a line segment is parallel to one side of the triangle and bisects the other two sides, then it bisects the third side. Also, the measure of the angle formed by the mid - segment and the sides of the triangle. Here, we use the angle - bisecting property (the angle formed by the mid - segment and the side of the triangle). We know that \(6x + 1=9x - 23\) (because of the equal - angle relationship in the triangle with the mid - segment).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides of the equation \(6x + 1=9x - 23\).
\(6x-6x + 1=9x-6x - 23\)
\(1 = 3x-23\)
Add \(23\) to both sides:
\(1 + 23=3x-23 + 23\)
\(24 = 3x\)
Divide both sides by \(3\):
\(x=\frac{24}{3}\)

Answer:

\(8\)