Question

AOB is a straight line. OC is a ray. OD and OE are the bisectors of Angle COA
and Angle COB respectively then what will be m Angle DOE?​

Answer 1

Step-by-step explanation:

your answer is in the pic

Answer 2

$\underline { Given :}$

$AOB \: is \: a \: straight \:line . OC \: is \: a \:ray.\\OD \: and \: OE \: are \: the \: bisectors \:of\\\angle {COA} \:and \: \angle {COB} \: respectively.$

$\red {To \: find \angle { DOE} = ? }$

$\underline { Proof:}$

$\angle {AOB} = 180\degree \: ( Straight \:angle )$

$\implies \angle { AOC} + \angle { COB} = 180\degree \: ( Linear \:pair )$

$\implies ( \angle { AOD} + \angle { DOC} )+(\angle { COE} + \angle { EOB}= 180\degree \:$

$\implies ( x + x ) + ( y + y ) = 180\degree$

$Given \: \blue { (\angle { AOD} = \angle { DOC} ) = x ) }$

$\blue {(\angle { COE} = \angle { EOB} = y )}$

$\implies 2x + 2y = 180\degree$

$\implies 2(x+y) = 180\degree$

$\implies x+y = \frac{180\degree}{2}$

$\implies \angle {DOE} = 90\degree$

Therefore.,

$\red { \angle {DOE} } \green { = 90\degree}$

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