m∠RSV = 3x + 5, m∠RST = 8x - 14 given
m∠RSV ≅ m∠VST definition of segment bisector
m∠RSV + m∠VST = m∠RST angle addition postulate
(3x + 5) + (3x + 5) = (8x - 14) substitution
6x + 10 = 8x - 14 simplify (added like terms)
10 = 2x - 14 subtraction property of equality
24 = 2x addition property of equality
12 = x division property of equality
Answer: x = 12