Question 1046706


< {{{AOC}}} and < {{{BOC}}} are supplementary ...................given
rays {{{OE}}} and {{{OD}}} bisect  < {{{BOC }}} and < {{{AOC}}} respectively

to prove: <{{{ DOE=90}}}°

proof:
.............statement........................-----------------..................reason

< {{{AOC + BOC =  180}}}°..............................................given

rays {{{OE}}} and {{{OD}}} bisect  < {{{BOC }}} and < {{{AOC}}} respectively....................given

  {{{(1/2) AOC + (1/2)BOC = (1/2)180}}}°

 {{{(1/2)AOC + (1/2)BOC = 90}}}°

=> < {{{DOC =  (1/2)AOC}}} and   < {{{COE = (1/2)BOC}}}

=> < {{{DOC +COE = 90}}}°......................{{{OE}}} and {{{OD}}} bisect  < {{{BOC }}} and < {{{AOC}}}
 
=> < {{{DOE = 90}}}°