Question

point z is the in - center of triangle rst. what is the value of x? (5x - 9)° 16°

Explanation:

Step1: Recall in - center property

The in - center of a triangle is the point of intersection of the angle bisectors of the triangle. So, the two angles formed by the angle bisector at vertex S are equal. That is, \(5x−9 = 16\).

Step2: Solve the equation for x

Add 9 to both sides of the equation: \(5x=16 + 9\). So, \(5x=25\).

Step3: Isolate x

Divide both sides of the equation \(5x = 25\) by 5. We get \(x=\frac{25}{5}=5\).

Answer:

\(x = 5\)