Question

the diagonals of rectangle ABCD intersect each other at O . if angle AOD is 30 then find angle OCD

Answer 1

● Given in Rectangle ABCD

=> angle(AOD) = 30

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ᴥ We know that,

=> angle(AOD) + angle(DOC) = 180 _________________[ Linear Pair ]

=> 30 + angle(DOC) = 180 ____[ Given ]

=> angle(DOC) = 150 _________[ Eq(1) ]

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{ ◢ Since Diagonal of Rectangle are equal and they bisect each other }

ᴥ Then,

=> OA = OB = OC = OD

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ᴥ NOW,

△DOC

{◢ Angles opposite to equal sides of a triangle are equal }

ᴥ Then,

=> angle(ODC) = angle(OCD)

ᴥ LET'S

=> angle(ODC) = angle(OCD) = X

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Again In △DOC

ᴥ We know that,

[angle(DOC)+angle(ODC)+angle(OCD)] = 180

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ᴥ Plug the all values we get,

=> 150 + X + X = 180

=> 150 + 2X = 180

=> 2X = 30

=> X = 15 ________________[ANSWER]

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ᴥ HENCE,

=> ANGLE(OCD) = 15 _________________[ANSWER]

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