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=900−350=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=12×1800−1100=350
∴ y = ∠BAC=350
[Interior alternate angles]
Also, x=900−y
[ ∴∠C=900=x+y ]
⇒x=900−350=550
Hence, x=550 and y=350