Question

1. solve for x. 35 21 x + 1 15

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 \(\frac{35}{15}=\frac{21}{x + 1}\).

Step2: Cross - multiply

Cross - multiplying gives us \(35(x + 1)=15\times21\).
Expanding the left - hand side: \(35x+35 = 315\).

Step3: Solve for \(x\)

Subtract 35 from both sides: \(35x=315 - 35\), so \(35x=280\).
Divide both sides by 35: \(x=\frac{280}{35}\).

Answer:

\(x = 8\)