sum of angles of a quadrilateral is 360° – Discussion Forum

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Virat

Asked: October 3, 2026In: Class 9 Maths

You know that the sum of angles of a quadrilateral is 360°, even for a non-convex quadrilateral. (Recall the proof.) Now consider a self-intersecting quadrilateral ABCD, where AB and CD intersect at point E. Show that ∠A + ∠B + ∠C + ∠D < 360°. Can you construct ABCD such that ∠A + ∠B + ∠C + ∠D = 2°?

In triangles EAD and EBC, vertical angles at E are equal, so the four vertex angles sum to 360° – 2∠AED < 360°. Yes, make angle E nearly 179° so the remaining sum equals 2°. Cbse released Class 9 Ganita Manjari ...