Class 8 Maths Chapter 4 Exploring Some Geometric Themes MCQs with Solutions

Geometry becomes easier when students understand shapes, patterns, and their properties instead of only remembering definitions. Exploring Some Geometric Themes in Class 8 Maths Ganita Prakash Part 2 introduces students to important geometrical ideas and improves their ability to observe and reason with figures.

Practicing CBSE Board Class 8 Maths Chapter 4 Exploring Some Geometric Themes MCQs with Answers helps students revise key concepts and check their understanding through different question patterns. These MCQs are useful for quick revision and building confidence before exams.

Students who want more chapter-wise practice can also explore Class 8 MCQs for other subjects. Regular practice of Class 8 Maths MCQs helps improve accuracy, strengthen concepts, and develop better problem-solving skills. A strong understanding of basic concepts and regular chapter-wise practice helps students build confidence and improve their overall Maths preparation.

Chapter 4 Exploring Some Geometric Themes Class 8 Maths MCQs with Answers

Practice these hard-level MCQs to improve your understanding of geometric concepts, properties, reasoning, and application-based problems from Exploring Some Geometric Themes.

Q. If two angles are complementary and one angle is three times the other, find the larger angle.

A. 45°
B. 60°
C. 67.5°
D. 75°

Answer: C. 67.5°

Explanation: Complementary angles add up to 90°. Let the smaller angle be x, so x + 3x = 90°. Therefore, x = 22.5° and the larger angle is 67.5°.

Q. A polygon has a total interior angle sum of 900°. How many sides does the polygon have?

A. 5 sides
B. 6 sides
C. 7 sides
D. 8 sides

Answer: C. 7 sides

Explanation: The sum of interior angles of a polygon is (n − 2) × 180°. Solving (n − 2) × 180 = 900 gives n = 7.

Q. If each interior angle of a regular polygon is 135°, identify the polygon.

A. Pentagon
B. Hexagon
C. Octagon
D. Decagon

Answer: C. Octagon

Explanation: Each exterior angle = 180° − 135° = 45°. Number of sides = 360° ÷ 45° = 8, so it is an octagon.

Q. In a triangle, two angles are 45° and 65°. Find the third angle.

A. 60°
B. 70°
C. 80°
D. 90°

Answer: B. 70°

Explanation: The sum of angles in a triangle is 180°. Third angle = 180° − (45° + 65°) = 70°.

Q. If a quadrilateral has three angles measuring 85°, 95°, and 110°, find the fourth angle.

A. 60°
B. 70°
C. 80°
D. 90°

Answer: B. 70°

Explanation: The sum of all angles of a quadrilateral is 360°. Fourth angle = 360° − 290° = 70°.

Q. The exterior angle of a regular polygon is 24°. How many sides does it have?

A. 12
B. 15
C. 18
D. 20

Answer: B. 15

Explanation: Number of sides of a regular polygon = 360° ÷ exterior angle = 360 ÷ 24 = 15.

Q. Which property is always true for a rectangle but not for every parallelogram?

A. Opposite sides are equal
B. Opposite angles are equal
C. All angles are 90°
D. Diagonals bisect each other

Answer: C. All angles are 90°

Explanation: Every rectangle has four right angles, but a general parallelogram does not always have 90° angles.

Q. A square is also considered a rectangle because:

A. It has unequal sides
B. It has four right angles
C. Its diagonals are always different
D. It has only one pair of parallel sides

Answer: B. It has four right angles

Explanation: A square satisfies the properties of a rectangle because it has four 90° angles and opposite sides parallel.

Q. Which statement about a rhombus is always correct?

A. All angles are equal
B. All sides are equal
C. Diagonals are always equal
D. It has no parallel sides

Answer: B. All sides are equal

Explanation: A rhombus always has four equal sides, but its angles and diagonals are not necessarily equal.

Q. If two lines intersect, the vertically opposite angles are:

A. Always unequal
B. Always equal
C. Always 90°
D. Always 180°

Answer: B. Always equal

Explanation: When two lines intersect, the opposite angles formed are called vertically opposite angles and they are equal.

Q. A regular polygon has 12 sides. Find each exterior angle.

A. 20°
B. 25°
C. 30°
D. 45°

Answer: C. 30°

Explanation: Each exterior angle = 360° ÷ number of sides = 360° ÷ 12 = 30°.

Q. The diagonals of a square:

A. Are unequal and parallel
B. Are equal and bisect each other at right angles
C. Never meet each other
D. Divide the square unequally

Answer: B. Are equal and bisect each other at right angles

Explanation: The diagonals of a square are equal in length and intersect each other at 90°.

Q. If two supplementary angles are equal, each angle measures:

A. 45°
B. 60°
C. 90°
D. 120°

Answer: C. 90°

Explanation: Supplementary angles add up to 180°. If both are equal, each angle is 180° ÷ 2 = 90°.

Q. Which quadrilateral has exactly one pair of parallel sides?

A. Square
B. Rectangle
C. Trapezium
D. Rhombus

Answer: C. Trapezium

Explanation: A trapezium is a quadrilateral that has one pair of opposite sides parallel.

Q. The sum of all exterior angles of any polygon is:

A. 90°
B. 180°
C. 270°
D. 360°

Answer: D. 360°

Explanation: The total measure of exterior angles of every polygon is always 360°.

Q. A triangle has sides 8 cm, 8 cm, and 10 cm. It is:

A. Scalene triangle
B. Isosceles triangle
C. Equilateral triangle
D. Right triangle only

Answer: B. Isosceles triangle

Explanation: A triangle with exactly two equal sides is called an isosceles triangle.

Q. A line that divides a figure into two identical halves is called:

A. Parallel line
B. Line of symmetry
C. Diagonal
D. Radius

Answer: B. Line of symmetry

Explanation: A line of symmetry divides a figure into two equal and matching parts.

Q. How many lines of symmetry does a square have?

A. 1
B. 2
C. 3
D. 4

Answer: D. 4

Explanation: A square has four lines of symmetry: two diagonals and two lines through the middle of opposite sides.

Q. If a circle has radius 9 cm, its diameter is:

A. 9 cm
B. 12 cm
C. 18 cm
D. 27 cm

Answer: C. 18 cm

Explanation: Diameter is twice the radius. Therefore, diameter = 2 × 9 = 18 cm.

Q. Which point is equally distant from all points on a circle?

A. Vertex
B. Centre
C. Edge
D. Diameter

Answer: B. Centre

Explanation: The centre of a circle is always at an equal distance from every point on the circle.

Q. A triangle cannot have:

A. Two acute angles
B. One right angle
C. Two obtuse angles
D. Three sides

Answer: C. Two obtuse angles

Explanation: A triangle cannot contain two obtuse angles because their sum would exceed 180°.

Q. If two parallel lines are cut by a transversal, corresponding angles are:

A. Equal
B. Unequal always
C. Supplementary always
D. Zero

Answer: A. Equal

Explanation: Corresponding angles formed by a transversal cutting parallel lines are always equal.

Q. A quadrilateral with all sides equal and all angles equal is:

A. Rhombus only
B. Rectangle only
C. Square
D. Trapezium

Answer: C. Square

Explanation: A square has all equal sides and all angles equal to 90°.

Q. A polygon with 10 sides is called:

A. Hexagon
B. Octagon
C. Decagon
D. Pentagon

Answer: C. Decagon

Explanation: A polygon having ten sides is known as a decagon.

Q. If an angle measures more than 90° but less than 180°, it is:

A. Acute angle
B. Right angle
C. Obtuse angle
D. Straight angle

Answer: C. Obtuse angle

Explanation: An obtuse angle is greater than 90° but smaller than 180°.

Q. Which shape has rotational symmetry of order 4?

A. Square
B. Rectangle
C. Semicircle
D. Kite

Answer: A. Square

Explanation: A square matches itself four times during one complete rotation, so its rotational symmetry order is 4.

Q. Two angles forming a linear pair always add up to:

A. 90°
B. 120°
C. 180°
D. 360°

Answer: C. 180°

Explanation: A linear pair consists of two adjacent angles whose measures always add up to 180°.

Q. The longest chord of a circle is:

A. Radius
B. Diameter
C. Arc
D. Sector

Answer: B. Diameter

Explanation: The diameter passes through the centre of a circle and is the longest possible chord.

Q. If all sides and all angles of a polygon are equal, it is called:

A. Irregular polygon
B. Regular polygon
C. Open figure
D. Curved figure

Answer: B. Regular polygon

Explanation: A regular polygon has all sides equal and all interior angles equal.

Q. A student observes that the same geometric pattern appears after turning a design by a certain angle. Which mathematical idea is being applied?

A. Area calculation only
B. Rotational symmetry
C. Ratio comparison
D. Linear measurement

Answer: B. Rotational symmetry

Explanation: Rotational symmetry occurs when a shape matches its original position after being rotated by a certain angle. It helps students understand patterns, transformations, and geometric relationships.

Chapter 4 Exploring Some Geometric Themes At a Glance

Important Concepts From Chapter 4 Exploring Some Geometric Themes

Geometric Shapes: Geometric shapes are an important part of this chapter. Students learn how different figures are formed and how their properties help us identify and compare them. Understanding shapes builds the foundation for advanced Geometry concepts.

Lines and Angles: Lines and angles help students understand the structure of different figures. Learning angle relationships makes it easier to solve problems based on measurements, patterns, and geometrical arrangements.

Properties of Triangles: Triangles are one of the most important shapes in Geometry. This chapter helps students explore their sides, angles, and important relationships that are useful for solving different mathematical problems.

Quadrilaterals and Other Figures: Students learn about different figures and their properties. Understanding these concepts improves logical thinking and helps students solve Geometry questions with better accuracy.

Geometrical Reasoning: Geometry is not only about remembering formulas. Students also learn how to observe figures, find patterns, and use reasoning to reach correct answers.

How to Score Better in Chapter 4 Exploring Some Geometric Themes MCQs

Geometry questions become simple when concepts are clear. Follow these tips while preparing this chapter:

• Revise important terms and properties before attempting questions.
• Understand the reason behind every rule instead of memorising.
• Observe diagrams carefully before answering.
• Practice different types of Geometry-based MCQs.
• Pay attention to small details like angles, sides, and measurements.
• Review mistakes to understand weak areas.

A clear understanding of basic concepts helps students solve both simple and application-based questions confidently.