Question 21 - End-of-Chapter Exercises - Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja
Last updated at May 26, 2026 by Teachoo
End-of-Chapter Exercises
Question 1
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Class 9
Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja
- Definitions
- Symmetries of Circle
- Number of Circles
- Exercise Set 5.1
- Think, Draw and Infer (Page 98)
- Angle Subtended by Chords
- Exercise Set 5.2
- Mid-points and Perpendicular Bisectors of Chords
- Exercise Set 5.3
- Distance of Chords from the Centre
- Exercise Set 5.4
- Distance of unequal chords from center
- Exercise Set 5.5
- Angle subtended by an arc
- Exercise Set 5.6
- Concyclicity of Points and Cyclic Quadrilateral
- Theorems (and their Proofs)
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End-of-Chapter Exercises
Transcript
Question 21 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). Let’s draw the figure Let CD be extended to point E We need to prove exterior angle at any vertex is equal to the interior opposite angle So, we need to prove ∠ ADE = ∠ ABC Note: In question it is given ∠ CDE = ∠ ABC, that’s a typo. It should be ∠ ADE = ∠ ABC Note: In question it is given ∠ CDE = ∠ ABC, that’s a typo. It should be ∠ ADE = ∠ ABC Now, we know that Opposite angles of cyclic quadrilateral are supplementary So, we can write ∠ ADC + ∠ ABC = 180° Also, since CE is a line By linear pair ∠ ADE + ∠ ADC = 180° Comparing (1) & (2) ∠ ADC + ∠ ABC = ∠ ADE + ∠ ADC ∠ ABC = ∠ ADE + ∠ ADC – ∠ ADC ∠ ABC = ∠ ADE Thus, we proved exterior angle at any vertex is equal to the interior opposite angle Hence proved
