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Piyush365
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Asked: 2026-10-05T09:33:47+00:00 In:

Show that the sum of angles of a non-planar quadrilateral is always less than 360°. Can you find a non-planar quadrilateral ABCD for which ∠A + ∠B + ∠C + ∠D = 2°? (Hint: Think of a diagonal, say AC, as a hinge around which triangles ABC and ADC can rotate.) What happens to each angle of ABCD as you do this rotation?

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Rotating △ABC and △ADC along hinge AC strictly reduces ∠A and ∠C below face angle sums, making the total sum < 360°. Yes, using very sharp triangles folded nearly flat gives a 2° total angle sum.

Cbse Class 9 Maths Ganita Manjari Part 2 Solutions
Class 9 maths ganita manjari part 2 chapter 12 question answer

cbse class 9 maths ganita manjari part 2 solutionsclass 9 maths ganita manjari part 2 chapter 12 question answerganita manjari part 2 chapter 12 quadrilaterals solutionshinge around which triangles abc and adc can rotatenon-planar quadrilateral abcdthe sum of angles of a non-planar quadrilateral
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    1. Folding along diagonal AC treats AC as a spatial hinge between triangles △ABC and △ADC. By 3D angle inequalities, the spatial angle is strictly less than the sum of its planar face angles: ∠A < ∠BAC + ∠CAD and ∠C < ∠BCA + ∠ACD. Since ∠B and ∠D remain unchanged, the four angles sum to strictly less than 360°. Yes, folding two extremely narrow triangles nearly flat yields a sum of exactly 2°.

       

      For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)

      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-12/

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