Question

solve for x. 24 10 2x - 5 21 answer

Explanation:

Step1: Apply the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the adjacent sides. So, we have the proportion \(\frac{10}{24}=\frac{2x - 5}{21}\).

Step2: Cross - multiply

Cross - multiplying gives us \(10\times21 = 24\times(2x - 5)\).

$$210=48x-120$$

Step3: Solve for \(x\)

Add \(120\) to both sides: \(210 + 120=48x\), so \(330 = 48x\). Then divide both sides by \(48\): \(x=\frac{330}{48}=\frac{55}{8}=6.875\).

Answer:

\(x = 6.875\)