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Piyush365
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Asked: 2026-10-05T09:34:09+00:00 In:

Sum of angles of a polygon. What is the sum of angles of a (planar non-self-intersecting) n-gon? We know that the answer is 180° for n = 3 and 360° for n = 4. Find the next few values. Then find a formula in terms of n and prove it.

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For n = 5, sum is 540°; for n = 6, 720°; for n = 7, 900°. General formula: (n – 2) × 180°. Proof: Drawing all diagonals from a single vertex divides the n-gon into n – 2 triangles, each summing to 180°.

Cbse released Class 9 Ganita Manjari Part 2 book
Chapter 12 Quadrilaterals (Ganita Manjari 2) Solutions

angles of a polygoncbse class 9 maths ganita manjari part 2 solutionsclass 9 ganita manjari part 2 chapter 12 page 81 question answerfind a formula in terms of n and prove itganita manjari part 2 chapter 12 solutionsknow that the answer is 180° for n = 3 and 360°
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    1. For n = 5, the sum of interior angles is 540°; for n = 6, it is 720°; for n = 7, it is 900°. The general formula for an n-gon is (n – 2) × 180°. Proof: Choose any single vertex and draw all possible diagonals to the other vertices. This partitions the non-self-intersecting n-gon into exactly n – 2 non-overlapping triangles. Since the angles of each triangle add up to 180°, the total sum is (n – 2) × 180°.

       

      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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