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Polygons Quiz - CBSE Class 9 Mathematics

Free practice quiz: Polygons (CBSE Class 9 Mathematics). 20 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 20 multiple-choice questions on Polygons, and 20 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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What a Polygon Is

  • A polygon is a simple closed figure made only of straight line segments, called sides.
  • Sides meet only at their endpoints, called vertices, and no two sides cross each other.
  • A polygon needs at least three sides. Curved or open figures are not polygons.

Common mistake: Calling a circle, a figure with a curved edge, or an open shape a polygon. Every side must be straight and the figure closed.

Naming Polygons by Sides

  • A polygon is named by its number of sides, often using a Greek prefix: tri, quadri, penta, hexa, hepta, octa, deca.
  • For example, an octagon has 8 sides, a nonagon has 9 sides and a decagon has 10 sides.
  • A polygon with n sides also has n vertices and n interior angles.
Sides, vertices and angles
\[\text{sides} = \text{vertices} = \text{interior angles} = n\]

Common mistake: Mixing up hexa and hepta, or penta and hexa. Learn the prefixes in order and count the sides carefully.

Convex, Concave, Regular, Irregular

  • Convex: every interior angle is less than a straight angle, and all diagonals lie inside the polygon.
  • Concave: at least one interior angle is reflex (more than a straight angle), so part of the figure caves inward.
  • Regular: all sides equal and all angles equal. If either condition fails, the polygon is irregular.

Common mistake: Thinking equal sides alone make a polygon regular. A rhombus has equal sides, but its angles may differ, so it may not be regular.

Interior and Exterior Angle Sums

  • From one vertex, draw diagonals to split an n-sided polygon into (n - 2) triangles.
  • Each triangle's angles add up to 180°, or two right angles. So the interior sum is (n - 2) × 180°.
  • For exterior angles, extend each side in the same direction around the polygon and take one exterior angle per vertex.
Interior angle sum
\[S = (n-2) \times 180^\circ\]
Each interior angle of a regular polygon (S is the interior angle sum above)
\[\text{each angle} = \frac{S}{n} = \frac{(n-2) \times 180^\circ}{n}\]
Exterior angle sum (convex, one angle per vertex, sides extended in one direction)
\[\text{sum of exterior angles} = 360^\circ\]
Interior and exterior angle at the same vertex
\[\text{interior} + \text{exterior} = 180^\circ\]

Common mistake: Using n × 180° instead of (n - 2) × 180°. The polygon splits into (n - 2) triangles, not n triangles.

Counting Diagonals

  • A diagonal joins two vertices that are not next to each other.
  • From each vertex, you can draw (n - 3) diagonals. Each diagonal is counted twice, so divide by 2.
Number of diagonals
\[D = \frac{n(n-3)}{2}\]

Common mistake: Forgetting to divide by 2, which counts each diagonal twice, once from each of its two end vertices.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is a polygon?

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    Answer: B. A shape with straight sides

    A polygon is defined as a flat shape with straight sides that are fully closed.

  2. What is the sum of the interior angles of a triangle?

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    Answer: B. 180 degrees

    The sum of the interior angles of a triangle always equals 180 degrees.

  3. What type of polygon is a hexagon?

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    Answer: D. 6-sided

    A hexagon is a polygon that has six sides.

  4. What is the main characteristic of a convex polygon?

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    Answer: B. All vertices point outward

    A convex polygon is characterized by having all its vertices pointing outward, meaning all interior angles are less than 180 degrees.

  5. What is the sum of the interior angles of a pentagon?

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    Answer: B. 540 degrees

    The sum of the interior angles of a pentagon can be calculated using the formula (n-2) × 180, which for 5 sides equals 540 degrees.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Which of the following is a polygon?
  2. How many sides does a quadrilateral have?
  3. Which of the following is true about polygons?
  4. If a polygon has 'n' sides, what is the formula to calculate the sum of its interior angles?
  5. What kind of polygon has all sides of equal length and all angles equal?
  6. How many sides does a pentagon have?
  7. Which of the following statements is true?
  8. A heptagon has how many sides?
  9. Which of the following polygons is classified as a concave polygon?
  10. What is the difference between a regular and irregular polygon?
  11. If a polygon has 12 sides, what is it called?
  12. Which of the following has the greatest number of sides?
  13. A polygon cannot have which of the following?
  14. What type of angles make a polygon concave?
  15. How many diagonals does a hexagon have?

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