In W, RS is congruent to TV. Find RS.

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