Question

An exterior angle of a cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle, to prove the theorem complete the activity.

Given:  ABCD is cyclic,

`square` is the exterior angle of  ABCD

To prove: ∠DCE ≅ ∠BAD

Proof: `square` + ∠BCD = `square`    .....[Angles in linear pair] (I)

 ABCD is a cyclic.

`square` + ∠BAD = `square`     ......[Theorem of cyclic quadrilateral] (II)

By (I) and (II)

∠DCE + ∠BCD = `square` + ∠BAD

∠DCE ≅ ∠BAD

Answer 1

Proof: 

Given:  ABCD is cyclic,

∠DCE is the exterior angle of  ABCD

To prove: ∠DCE ≅ ∠BAD

Proof: ∠DCE + ∠BCD = 180°    .....[Angles in linear pair] (I)

 ABCD is a cyclic.

∠BCD + ∠BAD = 180°     ......[Theorem of cyclic quadrilateral] (II)

By (I) and (II)

∠DCE + ∠BCD = ∠BCD + ∠BAD

∠DCE ≅ ∠BAD