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Question

In each of the figures given below, ABCD is a rectangle. Find the values of x and y in each case.


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Solution

Answer (i) ABCD is a rectangle.
The diagonals of a rectangle are congruent and bisect each other. Therefore, in​ AOB we have:
OA = OB
OAB=OBA=350
x=900350=550
And AOB=1800(350+350)=1100
y=AOB=1100
[Vertically opposite angles]
Hence, x=550andy=1100
(ii) In AOB we have:
OA = OB
Now, OAB=OBA=12×18001100=350
y = BAC=350
[Interior alternate angles]
Also, x=900y
[ C=900=x+y ]
⇒​x=900350=550
Hence, x=550 and y=350

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