Q. 175.0( 2 Votes )

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

Answer :

∠FDC + ∠CDA = 180^{o} (Linear pair)

80^{o} + ∠CDA = 180^{o}

∠CDA = 100^{o}

Since, ABCD is a cyclic quadrilateral

∠ADC + ∠ABC = 180^{o}

100^{o} + ∠ABC = 180^{o}

∠ABC = 80^{o}

Now,

∠ABC + ∠ABF = 180^{o} (Linear pair)

80^{o} + x = 180^{o}

x = 180^{o} – 80^{o}

= 100^{o}

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