Question

what is rs? rs =

Explanation:

Step1: Identify the theorem (Angle Bisector Theorem for distances from a point on the angle bisector to the sides)

Since \( \angle T \) is bisected, and \( TU \perp RU \), \( TS \perp RS \), by the Angle Bisector Theorem, the distances from \( R \) to the sides of the angle (i.e., \( RU \) and \( RS \)) are equal. So we set \( 7v = v + 60 \).

Step2: Solve for \( v \)

Subtract \( v \) from both sides: \( 7v - v = v + 60 - v \)
\( 6v = 60 \)
Divide both sides by 6: \( v = \frac{60}{6} = 10 \)

Step3: Find \( RS \)

Substitute \( v = 10 \) into \( RS = v + 60 \):
\( RS = 10 + 60 = 70 \)

Answer:

\( 70 \)