Question

what is the value of v? diagram of a geometric figure with right angles, segments labeled 11, angles labeled 4v and v + 45°

Explanation:

Step1: Apply the Angle Bisector Theorem

Since \(RU = RS = 11\) and \(RT\) is the angle - bisector (the distances from a point on the angle - bisector to the sides of the angle are equal, here \(RU\perp TU\) and \(RS\perp TS\)), we have \(4v=v + 45\).

Step2: Solve the equation for \(v\)

Subtract \(v\) from both sides of the equation \(4v=v + 45\).
\(4v−v=v + 45−v\)
\(3v=45\)
Divide both sides by 3: \(v=\frac{45}{3}\)

Answer:

\(15\)