In a cyclic quadrilateral, opposite interior angles are supplementary. Since an exterior angle and its adjacent interior angle are also supplementary, the exterior angle equals the opposite interior angle. Hence, ∠CDE = ∠ABC.
Let ABCD be a cyclic quadrilateral. Explain why the exterior angle at any vertex is equal to the interior opposite angle (e.g., ∠CDE = ∠ABC, where E is a point on the extension of side CD).
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Let ABCD be a cyclic quadrilateral and let CD be extended to E. Then ∠CDE and ∠CDA form a linear pair, so their sum is 180°. Also, opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
∠ABC + ∠CDA = 180°
and
∠CDE + ∠CDA = 180°.
Hence,
∠CDE = ∠ABC.
Thus, the exterior angle of a cyclic quadrilateral is equal to its interior opposite angle.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/