Question

1. iu

find each measure.
p

Explanation:

Step1: Apply the Angle Bisector Theorem (distance from a point to the sides of an angle)

Since \(R\) is the vertex of the angle and \(RT\perp\) one side, \(RI\perp\) the other side, and \(RU\) is the angle - bisector. 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 \(2x + 5=7x\).

Step2: Solve the equation \(2x + 5=7x\)

Subtract \(2x\) from both sides: \(5=7x - 2x\).
Simplify the right - hand side: \(5 = 5x\).
Divide both sides by \(5\): \(x = 1\).

Step3: Calculate the length of \(IU\)

Substitute \(x = 1\) into the expression for \(IU\). Since \(IU=7x\), then \(IU = 7\times1=7\).

Answer:

\(IU = 7\)