Mathematics
In the figure (i) given below, ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. Given that ∠BEF = 80°, find ∠ABC.
Circles
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Answer
ADFE is a cyclic quadrilateral as all vertices lie on the circumference of the circle.
∠ADF = ∠FEB = 80° (∵ exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.)
As opposite angles of a parallelogram are equal.
∠ABC = ∠ADC
From figure,
∠ADC = ∠ADF = 80°.
∴ ∠ABC = 80°.
Hence, the value of ∠ABC = 80°.
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