Q. 274.2( 5 Votes )

*ABCD* is a cyclic trapezium with *AD||BC.* If *∠**B*=70°, determine other three angles of the trapezium.

Answer :

Given that,

ABCD is a cyclic trapezium with AD ‖ BC and ∠B = 70^{o}

Since, ABCD is a quadrilateral

Then,

∠B + ∠D = 180^{o}

70^{o} + ∠D = 180^{o}

∠D = 110^{o}

Since, AD ‖ BC

Then,

∠A + ∠B = 180^{o} (Co. interior angle)

∠A + 70^{o} = 180^{o}

∠A = 110^{o}

Since, ABCD is a cyclic quadrilateral

Then, ∠A + ∠C = 180^{o}

110^{o} + ∠C = 180^{o}

∠C = 70^{o}

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