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About Polygons — Class 8 ICSE

Explore interior and exterior angles of regular and irregular polygons. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 11). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Polygons

  • Introduction to Polygons
  • Angle Sum Property
  • Properties of Parallelograms
  • Rectangle, Rhombus, and Square
  • Trapezium and Summary

Interactive lesson · about 20 minutes · checkpoint question after every unit

Polygons — solved examples for Class 8 ICSE

Example 1easy

What is the sum of interior angles of a quadrilateral?
  1. A)180°
  2. B)270°
  3. C)360°
  4. D)540°

Step-by-step solution

  1. A quadrilateral has 4 sides, so n = 4.
  2. Sum of interior angles:
    (n−2)×180°=(4−2)×180°=2×180°=360°(n - 2) × 180° = (4 - 2) × 180° = 2 × 180° = 360°

Answer: 360°

Example 2medium

Find the number of diagonals in a hexagon.
  1. A)6
  2. B)8
  3. C)9
  4. D)12

Step-by-step solution

  1. Number of diagonals formula:
    n(n−3)/2n(n - 3)/2
  2. For a hexagon (n = 6):
    6(6−3)/2=6×3/2=18/2=96(6 - 3)/2 = 6 × 3/2 = 18/2 = 9

Answer: 9

Example 3hard

The ratio of an interior angle to the exterior angle of a regular polygon is 7:2. Find the number of sides.
  1. A)8
  2. B)9
  3. C)10
  4. D)12

Step-by-step solution

  1. Let interior = 7k and exterior = 2k.
  2. They are supplementary:
    7k+2k=180°→9k=180°→k=20°7k + 2k = 180° → 9k = 180° → k = 20°
  3. Exterior angle = 2 × 20° = 40°.
  4. Number of sides:
    n=360°÷40°=9n = 360° ÷ 40° = 9

Answer: 9

Practice questions on Polygons

  1. Q1.easy

    A polygon with 5 sides is called a:
    1. A)Hexagon
    2. B)Pentagon
    3. C)Heptagon
    4. D)Octagon
    Show answer

    Answer: Pentagon

    Hint: 'Penta' means five in Greek.

  2. Q2.easy

    A regular polygon has:
    1. A)All sides equal only
    2. B)All angles equal only
    3. C)All sides and all angles equal
    4. D)No sides equal
    Show answer

    Answer: All sides and all angles equal

    Hint: 'Regular' means everything is equal — both sides and angles.

  3. Q3.easy

    What is the sum of exterior angles of any convex polygon?
    1. A)180°
    2. B)270°
    3. C)360°
    4. D)540°
    Show answer

    Answer: 360°

    Hint: This is the same for every convex polygon, no matter how many sides it has.

  4. Q4.medium

    The sum of interior angles of a polygon is 1080°. How many sides does it have?
    1. A)6
    2. B)7
    3. C)8
    4. D)9
    Show answer

    Answer: 8

    Hint: Set (n - 2) × 180° = 1080° and solve for n.

  5. Q5.medium

    Each exterior angle of a regular polygon is 40°. How many sides does it have?
    1. A)7
    2. B)8
    3. C)9
    4. D)10
    Show answer

    Answer: 9

    Hint: Each exterior angle of a regular polygon = 360° ÷ n. Rearrange to find n.

  6. Q6.medium

    Find the number of diagonals in a decagon (10-sided polygon).
    1. A)30
    2. B)35
    3. C)40
    4. D)45
    Show answer

    Answer: 35

    Hint: Use n(n - 3)/2 with n = 10.

  7. Q7.hard

    The interior angle of a regular polygon is 156°. Find the number of diagonals.
    1. A)54
    2. B)60
    3. C)65
    4. D)90
    Show answer

    Answer: 90

    Hint: First find the number of sides using the exterior angle, then use the diagonal formula.

  8. Q8.hard

    The number of diagonals of a polygon is 44. Find the number of sides.
    1. A)9
    2. B)10
    3. C)11
    4. D)12
    Show answer

    Answer: 11

    Hint: Solve n(n - 3)/2 = 44, which gives n(n - 3) = 88.

  9. Q9.hard

    An architect in Mumbai designs a building with a regular polygon-shaped floor plan. If the sum of interior angles is 2160°, what polygon shape is the floor?
    1. A)Dodecagon (12 sides)
    2. B)Tetradecagon (14 sides)
    3. C)Pentadecagon (15 sides)
    4. D)Hexadecagon (16 sides)
    Show answer

    Answer: Tetradecagon (14 sides)

    Hint: Use (n - 2) × 180° = 2160° and solve for n.

These are 9 of the 60 questions available for Polygons. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.