Question

what is the value of v? v =

Explanation:

Step1: Apply the Angle - Bisector Theorem for Distances

Since \(JH\) is the angle - bisector of \(\angle KJI\) and \(HK\perp JK\), \(HI\perp JI\), by the Angle - Bisector Theorem (the distance from a point on the angle - bisector to the two sides of the angle is equal), we have \(HK = HI\).

Step2: Set up the equation

We know that \(HK=v + 28\) and \(HI = 2v\). So, we can set up the equation \(v+28=2v\).

Step3: Solve the equation for \(v\)

Subtract \(v\) from both sides of the equation \(v+28=2v\).

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Answer:

\(28\)