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Polygons and Their Types Quiz - CBSE Class 8 Mathematics

Free practice quiz: Polygons and Their Types (CBSE Class 8 Mathematics). 20 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 20 multiple-choice questions on Polygons and Their Types, 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 Makes a Polygon

  • A polygon is a simple closed figure made only of straight line segments. Its sides meet only at endpoints.
  • Curved sides are not allowed. Open figures and self-crossing figures are not polygons.
  • Convex: every diagonal lies inside. Concave: at least one diagonal lies partly outside.

Common mistake: Calling a circle or a shape with one curved edge a polygon. Every side must be a straight line segment.

Naming and Regular Polygons

  • A polygon's name tells its number of sides. For example, a nonagon has 9 sides.
  • Any polygon has equally many sides, vertices and angles. A quadrilateral has 4 of each.
  • Regular means all sides equal AND all angles equal. If either condition fails, the polygon is irregular.
Sides, vertices and angles
\[\text{sides} = \text{vertices} = \text{angles} = n\]

Common mistake: Thinking equal sides alone make a polygon regular. A rhombus has equal sides but is not regular unless its angles are also equal.

Sum of Interior Angles

  • Diagonals drawn from one vertex split an n-sided polygon into (n − 2) triangles.
  • Each triangle's angles add to 2 right angles, so multiply the number of triangles by 2 right angles.
  • In a regular polygon all interior angles are equal, so divide the total by n.
Interior angle sum
\[S = (n-2)\times 2 \times 90^\circ\]
Each interior angle (regular)
\[\frac{(n-2)\times 2\times 90^\circ}{n}\]
Quadrilateral angle sum
\[\angle A+\angle B+\angle C+\angle D = 4\times 90^\circ\]

Common mistake: Using n triangles instead of (n − 2) triangles, which makes the total too large.

Sum of Exterior Angles

  • An exterior angle is formed by one side and the extension of the next side.
  • At each vertex, the interior and exterior angles form a straight line, so they add to 2 right angles.
  • For any convex polygon, the exterior angles always add to 4 right angles, whatever the number of sides.
Exterior angle sum
\[\text{Sum of exterior angles} = 4\times 90^\circ\]
Each exterior angle (regular)
\[e = \frac{4\times 90^\circ}{n}\]
Interior + exterior at a vertex
\[i + e = 2\times 90^\circ\]
Sides from exterior angle
\[n = \frac{4\times 90^\circ}{e}\]

Common mistake: Thinking the exterior angle sum grows with more sides. It is the same for every convex polygon.

Counting Diagonals

  • A diagonal joins two vertices that are not next to each other.
  • Each vertex joins to (n − 3) others. Halve the total, because each diagonal gets counted twice.
Number of diagonals
\[D = \frac{n(n-3)}{2}\]

Common mistake: Forgetting to divide by 2, or counting the sides as diagonals.

Exam tips

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

Sample questions

  1. Which of the following is a polygon?

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    Answer: B. A triangle

    A polygon is a closed figure made up of line segments. A triangle is a polygon with three sides.

  2. Identify the polygon with seven sides.

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    Answer: C. Heptagon

    A heptagon is a seven-sided polygon.

  3. If the sum of interior angles of a polygon is 1080 degrees, how many sides does it have?

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    Answer: C. 8

    Using the formula (n-2) * 180 = 1080, we solve for n: n-2 = 6, n = 8. Therefore, it's an octagon.

  4. A polygon has 15 sides. What is the sum of its exterior angles?

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    Answer: B. 360 degrees

    The sum of exterior angles of any polygon is always 360 degrees.

  5. Two angles of a quadrilateral are 110° and 100°. The other two angles are equal. Find the measure of each equal angle.

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    Answer: C. 75°

    The sum of angles in a quadrilateral is 360°. Let the equal angles be x. Then 110° + 100° + x + x = 360°. Solving for x gives x = 75°.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What is a quadrilateral?
  2. A polygon with 5 sides is called a...
  3. How many sides does a hexagon have?
  4. Which polygon has equal sides and equal angles?
  5. A decagon has how many angles?
  6. What is the sum of interior angles of a pentagon?
  7. Explain the difference between a regular and irregular hexagon.
  8. Can a polygon have curved sides?
  9. What is the measure of each interior angle of a regular pentagon?
  10. What is the measure of each exterior angle of a regular octagon?
  11. Determine the number of diagonals in a hexagon.
  12. Prove that the sum of the interior angles of a triangle is 180 degrees.
  13. If a polygon has n sides, what is the formula for the number of triangles that can be formed by joining any three vertices?
  14. Construct a proof showing that the sum of the exterior angles of a convex polygon is 360 degrees. Assume prior knowledge of triangle angle sum.
  15. A convex polygon has 20 sides. Find the sum of its interior angles. Then find the number of triangles that can be formed by joining the vertices, and explain the relationship between these two quantities.

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