Chapter 11 · Class 8 CBSE · MCQ Test
Geometric Explorations MCQ Test — Class 8 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Geometric Explorations — MCQ Questions
1Which of the following statements about the sum of interior angles of a polygon is true?
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Answer: The sum of interior angles of a polygon with 'n' sides is always (n-2) × 180°.
Hint: Recall the formula for the sum of interior angles of any polygon, which depends on the number of its sides.
Solution:
A polygon can be divided into (n-2) non-overlapping triangles by drawing diagonals from one vertex.
Since the sum of interior angles of one triangle is 180°, the sum of interior angles of a polygon with 'n' sides is (n-2) times 180°. — Sum = (n - 2) × 180°
2Rohan states, 'The sum of the exterior angles of any polygon, one at each vertex, is always 360°, regardless of the number of sides.' Is Rohan's statement correct?
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Answer: Yes, this is a fundamental property of all convex polygons.
Hint: Consider the relationship between interior and exterior angles at each vertex and how they contribute to the total turn around the polygon.
Solution:
For any convex polygon, if you traverse its perimeter and turn at each vertex by its exterior angle, you complete one full circle.
A full circle represents a total rotation of 360°. Therefore, the sum of the exterior angles of any convex polygon is always 360°.
3A quadrilateral has angles measuring 70°, 95°, and 110°. What is the measure of the fourth angle?
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Answer: 85°
Hint: Remember the sum of interior angles for any quadrilateral.
Solution:
The sum of the interior angles of any quadrilateral is 360°.
Let the unknown fourth angle be 'x'. So, 70° + 95° + 110° + x = 360°.
Adding the known angles: 275° + x = 360°.
Subtracting 275° from both sides: x = 360° - 275° = 85°.
4In a parallelogram ABCD, if ∠A = 65°, what is the measure of ∠C?
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Answer: 65°
Hint: Recall the properties of opposite angles in a parallelogram.
Solution:
One of the key properties of a parallelogram is that its opposite angles are equal.
In parallelogram ABCD, ∠A and ∠C are opposite angles.
Therefore, if ∠A = 65°, then ∠C must also be 65°.
5A polygon is described as 'a simple closed curve made up of only line segments'. Which of the following shapes fits this description?
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Answer: Triangle
Hint: Consider which of the options is formed exclusively by straight line segments, without any curves.
Solution:
The definition provided describes a polygon.
A circle, oval, and semicircle are all curved shapes, not made up of only line segments.
A triangle is a three-sided polygon, formed by three straight line segments connected end-to-end to form a closed figure.
6Reena is trying to identify a quadrilateral. She knows that its diagonals bisect each other and are perpendicular. Which type of quadrilateral is she most likely describing?
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Answer: Rhombus
Hint: Think about the specific properties of diagonals for different types of parallelograms.
Solution:
For a quadrilateral whose diagonals bisect each other, it must be a parallelogram.
Among parallelograms, if the diagonals are also perpendicular, the shape is either a rhombus or a square.
However, the description 'diagonals bisect each other and are perpendicular' is the defining characteristic of a rhombus. A square has this property too, but also has equal diagonals, which isn't explicitly mentioned as a required condition here, making rhombus the most direct answer.
7Which of the following statements about a square is INCORRECT?
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Answer: Its diagonals are not necessarily equal in length.
Hint: A square is a special type of rectangle and a special type of rhombus. Consider the diagonal properties of both.
Solution:
A square is a special type of parallelogram, a rectangle, and a rhombus.
Properties of a square include: all angles are 90°, all sides are equal, and diagonals bisect each other perpendicularly (like a rhombus).
Additionally, like a rectangle, the diagonals of a square are always equal in length. Therefore, the statement 'Its diagonals are not necessarily equal in length' is incorrect.
8Consider a regular hexagon. What is the measure of each interior angle?
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Answer: 120°
Hint: First, find the sum of interior angles for a hexagon, then divide by the number of angles, as it's a regular polygon.
Solution:
A hexagon has 6 sides (n=6). The sum of interior angles of a polygon is (n-2) × 180°.
Sum of interior angles = (6-2) × 180° = 4 × 180° = 720°.
Since it is a regular hexagon, all its interior angles are equal. So, each interior angle = Sum / n = 720° / 6.
Each interior angle = 120°.
9An object has 6 faces and 8 vertices. If it is a polyhedron, how many edges does it have, according to Euler's formula?
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Answer: 12
Hint: Recall Euler's formula, which relates the number of faces (F), vertices (V), and edges (E) of any polyhedron.
Solution:
Euler's formula for polyhedra states: F + V - E = 2, where F is the number of faces, V is the number of vertices, and E is the number of edges.
Given F = 6 and V = 8, we can substitute these values into the formula: 6 + 8 - E = 2.
Simplify the equation: 14 - E = 2.
To find E, rearrange the formula: E = 14 - 2 = 12.
10A polygon has at least one interior angle greater than 180°. What type of polygon is it?
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Answer: Concave polygon
Hint: Think about the definition of convex and concave polygons, particularly how they relate to their interior angles and diagonals.
Solution:
A convex polygon is one where all interior angles are less than 180°, and all diagonals lie entirely inside the polygon.
A concave polygon (or non-convex polygon) is one where at least one interior angle is greater than 180° (a reflex angle).
In a concave polygon, at least one part of a diagonal lies outside the polygon. Therefore, the description matches a concave polygon.
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Tips for Geometric Explorations MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Geometric Explorations MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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