RS = 11
Solution:
Arc RS and arc TV are congruent arcs in same circle.
So, the corresponding chords are RS and TV are congruent.
⇒ RS = TV (by the definition of congruent segments)
⇒ 5x - 9 = 2x + 3 (substitution)
Add 9 on both sides.
⇒ 5x - 9 + 9 = 2x + 3 + 9
⇒ 5x = 2x + 12
Subtract 2x from both sides.
⇒ 5x - 2x = 2x + 12 - 2x
⇒ 3x = 12
Divide by 3 on both sides, we get
⇒ x = 4
RS = 5x - 9
= 5(4) - 9
RS = 11
