Question

point z is the incenter of triangle rst. what is the value of x? x=2 x=3 x=5 x=8

Explanation:

Step1: Recall incenter property

The incenter of a triangle is the intersection of angle bisectors, so \( \angle ASZ=\angle CSZ \). Thus, \( 5x - 9 = 16 \).

Step2: Solve for \( x \)

Add 9 to both sides: \( 5x=16 + 9=25 \).
Divide by 5: \( x=\frac{25}{5}=5 \).

Answer:

\( x = 5 \) (corresponding to the option "x = 5")