Question

Prove that an exterior angle of a cyclic
quadrilateral is congruent to the angle opposite
to its adjacent interior angle.
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Answer 1

Given:

ABCD is a cyclic quadrilateral.

∠BCE is the exterior angle of ABCD

exterior angle of ABCD.

To prove:

∠BCE = ∠BAD

Proof:

BCE+ BCD = 180°

ABCD is a cyclic quadrilateral.

∠BAD + ∠BCD = 180°

∠BCE + ∠BCD = ∠BAD +∠BCD

∠BCE = ∠BAD

=> ∠BAD = ∠BAD ...hence proved

Answer 2

Answer:

Prove that an exterior angle of a cyclic

quadrilateral is congruent to the angle opposite

to its adjacent interior angle.