Question

what is the value of u?

Explanation:

Step1: Use the Angle - Bisector Theorem (HL ≅ JL, so angles are equal)

Since \(KH = KJ = 34\) and \(KI\) is a common side, by the Hypotenuse - Leg (HL) congruence criterion for right - triangles (\(\triangle HKI\) and \(\triangle JKI\)), \(\angle HIK=\angle JIK\). So, \(u + 30=4u\).

Step2: Solve the equation for \(u\)

Subtract \(u\) from both sides of the equation \(u + 30=4u\).
We get \(30=4u - u\).
Simplify the right - hand side: \(30 = 3u\).
Divide both sides by 3: \(u=\frac{30}{3}\).

Answer:

\(10\)