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 angles DOE ?​

Answer 1

$\underline { \blue {Given:}}$

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

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

$\underline { \blue {Proof:}}$

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

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

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

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

$and \: \blue { ( \angle {COE} = \angle {EOB} = y }$

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

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

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

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

Therefore.,

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

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