Q15 of 100 Page 17

In Fig. 16.187, ∠BAD=78°, ∠DCF=x° and ∠DEF=y°. Find the values of x and y.

We have,

∠BAD = 78o


∠DCF = xo


∠DEF = yo


Since, ABCD is a cyclic quadrilateral


∠BAD + ∠BCD = 180o


78o + ∠BCD = 180o


∠BCD = 102o


Now,


∠BCD + ∠DCF = 180o (Linear pair)


102o = x – 180o


x = 78o


Since,


DCEF is a cyclic quadrilateral


x + y = 180o


78o + y = 180o


y = 102o


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In a cyclic quadrilateral ABCD, if ∠A-∠C=60°, prove that the smaller of two is 60°.

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In Fig. 16.188, ABCD is a cyclic quadrilateral. Find the value of x.