Question

Sv is an angle bisector of rst. If mrsv = (3x+5) and mrst = (8x-14), find x.

Answer 1

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