Question

Given ABCD is cyclic.  DCE is an exterior

angle of ABCD.

To prove:  DCE =  BAD

Proof: m DCE + BCD = (Linear pair of angle) - (1)

ABCD is cyclic.

0  BAD + = 180 - (Theorem of ) - (2)

 from equation (1) & (2), we get

 DCE + = +  BCD

 DCE =

Answer 1

Answer:

BCE + ∠BCD = 180°…… (i) [Angles in a linear pair] ⟂ABCD is a cyclic quadrilateral. [Given] ∠BAD + ∠BCD = 180°………. (ii) [Opposite angles of a cyclic quadrilateral are supplementary] ∴ ∠BCE + ∠BCD = ∠BAD + ∠BCD [From (i) and (ii)] ∴ ∠BCE = ∠B