Question

SV is an angle bisector of ∠RST. If m∠RSV = (3x + 9)° and m∠RST = (8x − 26)°, find x.

Answer 1

C) Definition of Angle Bisector, x=22

Explanation:

`As\ we\ the\ question\ relates\ only\ about\ SV\ bisecting\ \angle RST,\ We\ may\ use\ the\\`
`C)Angle\ Bisector`

`From\ the\ information\ provided\ we\ know\ that,\\SV\ bisects\ \angle RST\ into\ \angle RSV\ and\ \angle VST.\\Hence,\\\angle RSV\ and\ \angle VST\ are\ equal\ as\ they\ are\ the\ bisected\ angles\ of\ the\ same\ angle.\\Hence,\\\angle RSV\ = \angle VST\\Hence,\\We\ know\ that:\\\angle RSV\ + \angle VST =\angle RST\\Hence,\\\angle RSV\ +\angle RSV\ = \angle RST\\2\angle RSV=\ \angle RST\\`

`Now\ from\ the\ information\ about\ the\ values\ of\ the\ angles\ provided\ in\ the\ question\ ,\\\angle RSV=(3x+9)\\\angle RST=(8x-26)\\Hence,\\2(3x+9)=(8x-26)\\6x+18=8x-26\\18+26=8x-6x\\2x=44\\x=22`