Question

1. find the value of x.

(5x - 24)°
(8x + 9)°

Explanation:

Step1: Use the triangle mid - segment theorem (angle relationship)

The triangle mid - segment theorem implies that \(8x + 9=5x - 24\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(8x-5x + 9=5x-5x - 24\), which simplifies to \(3x+9=-24\).
Subtract \(9\) from both sides: \(3x+9 - 9=-24 - 9\), so \(3x=-33\).
Divide both sides by \(3\): \(x=\frac{-33}{3}\).

Answer:

\(x = - 11\)