Question

point z is the incenter of triangle rst. what is the value of x? x = 2 x = 3 x = 5 x = 8 (5x - 9)° 16°

Explanation:

Step1: Recall incenter property

The incenter of a triangle is the intersection of angle bisectors, so \( \angle RSZ=\angle TSZ \). 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 \( x = 5 \))