Question 939781



if {{{ST}}} bisects angle {{{RSV}}} means divides angle into two equal parts, angle {{{RST}}} and angle {{{TSV}}}
it means {{{m}}} <{{{RSV}}}={{{m}}} <{{{RST}}}+{{{m}}} <{{{TSV}}}

   if   {{{m}}} < {{{RST =2x+3y}}}
      {{{m}}} < {{{TSV = 3x-y+2}}}
 
{{{m}}} < {{{RSV = 80}}} degrees 

and if {{{m}}} <{{{RSV}}}={{{m}}} <{{{RST}}}+{{{m}}} <{{{TSV}}}, then

{{{m}}} < {{{2x+3y=40}}}........eq.1
{{{m}}} < {{{ 3x-y+2=40}}}......eq.2
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solve the system:
{{{2x+3y=40}}}........eq.1
{{{ 3x-y+2=40}}}......eq.2....both sides multiply by {{{3}}}
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{{{2x+3y=40}}}........eq.1
{{{ 9x-3y+6=120}}}......eq.2.
------------------------------------add

{{{2x+cross(3y)+9x-cross(3y)+6=40+120}}}

{{{2x+9x+6=160}}}

{{{11x=160-6}}}

{{{11x=154}}}

{{{x=154/11}}}

{{{x=14}}}
     
go to {{{ 3x-y+2=40}}}......eq.2 substitute {{{14}}} for {{{x}}} and solve for {{{y}}}

{{{ 3*14-y+2=40}}}

{{{ 42-y+2=40}}}

{{{ 44-40=y}}}

{{{ 4=y}}}

so, the  {{{m}}} <{{{RST}}} and {{{m}}} <{{{TSV}}} is:


{{{m}}} < {{{RST =2x+3y}}}=>{{{m}}} < {{{RST =2*14+3*4}}}{{{m}}} < {{{RST =28+12}}}=>{{{m}}} < {{{RST =40}}}

{{{m}}} < {{{TSV = 3x-y+2}}}=>{{{m}}} < {{{TSV = 3*14-4+2}}}=>{{{m}}} < {{{TSV = 42-4+2}}}=>{{{m}}} < {{{TSV = 44-4}}}=>{{{m}}} < {{{TSV =40}}}