Question

2. Fig. 14.66. In a quad. ABCD, ext XCD=int. opp
ZA. Prove that quad. ABCD is a cyclic quad.
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Answer 1

Given : In a quad. ABCD, ext XCD = int. opp  ∠A.

To Find : Prove that quad. ABCD is a cyclic quad.

Solution:

ext XCD  + int ∠D = 180°  ( linear pair )

. ext XCD   =  int. opp  ∠A.

=>  int. ∠A.  + int ∠D = 180°

Hence Sum of opposite angle of Quadrilateral ABCD is 180°

=> ABCD is a cyclic Quadrilateral

QED

Hence Proved

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