Question 122016
Remember, the sum of an angle and it's complement is {{{90}}}, an angle and its. supplement is {{{180}}}.

If angle is {{{highlight( A )}}},  it's complement is angle {{{ C }}} , and the {{{sum}}} of an angle and it's supplement is angle {{{ S }}},  then we have:

{{{highlight( A ) + C + S = highlight(A) + 200 }}}  

Since {{{ C + highlight( A ) = 90 }}} and {{{ S + highlight( A ) = 180 }}}, then we will have:

{{{ C = 90 -  highlight( A ) }}} and {{{ S = 180- highlight( A ) }}},

So,


{{{highlight( A)+( 90 -  highlight( A )) + (180 - highlight( A )) = highlight( A ) + 200 }}}  

{{{cross(highlight( A))+ 90 -  cross(highlight( A )) + 180 - highlight( A ) = highlight( A ) + 200 }}}  

{{{cross(highlight( A)) -  cross(highlight( A )) - highlight( A )- highlight( A ) =  200 - 270 }}}  

{{{-2highlight(A) = -70}}}..........divide both sides by {{{-2}}}  

{{{highlight( A ) =  35  }}}  


it's complement {{{ C }}} is:

{{{ C = 90 -  highlight( A) }}}
{{{ C = 90 - 35  }}}
{{{ C = 55  }}}……………

 and and its. supplement {{{ S }}} is:

{{{  S = 180- highlight( A ) }}}

{{{  S  = 180 - 35  }}}

{{{  S = 145 }}}


Check:

{{{highlight( A ) + C + S = highlight( A ) + 200 }}}  
 
{{{35 + 55 + 145  = 35 + 200 }}}  

{{{235  =  235 }}}