Question

what is the value of s? s =

Explanation:

Step1: Apply angle - bisector theorem

Since the ray $IG$ is the angle - bisector of $\angle H IJ$ and $GH\perp IH$, $GJ\perp IJ$, we know that $GH = GJ$ (a point on an angle - bisector is equidistant from the sides of the angle).

Step2: Set up the equation

Set $2s=s + 27$.

Step3: Solve the equation

Subtract $s$ from both sides of the equation $2s=s + 27$. We get $2s−s=s + 27−s$, which simplifies to $s = 27$.

Answer:

$27$