non-planar quadrilateral abcd – Discussion Forum

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Piyush365

Asked: October 5, 2026In: Class 9 Maths

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?

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 ...