CBSE Class 5 Mathematics: Shapes and Angles NCERT Solutions

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NCERT Solutions PDF Class 5 PDF

This chapter, 'Shapes and Angles,' for CBSE Class 5 Mathematics, introduces students to fundamental geometric concepts. The NCERT Solutions cover identifying and differentiating between closed and open shapes, counting the number of sides in various polygons, and understanding how angles contribute to the overall shape. Students will explore different types of angles through visual examples and practice identifying equal angles marked in different colors within given figures. These solutions provide clear, step-by-step explanations to help students grasp these basic geometry principles, aiding in their understanding and revision for exams. The exercises focus on observation and comparison of shapes and their constituent angles.

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Quick info

BoardCBSE
ClassClass 5
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
Chapter2 Shapes And Angles

Chapter summary

Chapter 2, 'Shapes and Angles,' for Class 5 Mathematics NCERT Solutions, focuses on basic geometric understanding. It covers distinguishing between open and closed shapes, identifying the number of sides in polygons, and recognizing how different angles affect a shape's appearance. The solutions guide students through exercises involving visual analysis of shapes and angles, including comparing angles marked in various colors. This chapter builds foundational knowledge in geometry for young learners.

Learning outcomes

  • Understand the difference between open and closed shapes.
  • Identify and count the number of sides in simple polygons.
  • Recognize that angles determine the specific form of a shape.
  • Compare and identify equal angles within different shapes.
  • Differentiate shapes based on their angles.

Topics covered

Paper topics

  • Shapes
  • Angles
  • Open Shapes
  • Closed Shapes
  • Number of Sides
  • Polygons
  • Angle Comparison
  • Geometric Figures

Important topics

  • Identifying Open vs. Closed Shapes
  • Counting Sides of Polygons
  • Understanding the Role of Angles in Shapes
  • Comparing Equal Angles

PDF preview

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Questions and Solutions

Question 1

Rohini made a shape. Mohini asked: Is it a closed shape or an open shape? Rohini said: It is a closed shape. Mohini asked: How many sides are there? Rohini said: It has 6 sides.

Mohini made this. Now you give the answers.

  1. Is it a closed shape?
  2. Does it have 6 sides?
Solution:

1. Yes, the shape made by Mohini is a closed shape because all its sides are connected, forming a complete boundary.

2. Yes, the shape made by Mohini has 6 sides, just like the one Rohini made.

Question 2

But it is not the same as the one made by Rohini. So Mohini tried again. This is what she made.

  1. Is it a closed shape with 6 sides?
  2. Is it the same as one made by Rohini?
  3. Is there some way to say in what way these shapes are different?
  4. Mohini tried again but got different shapes. Guess and make two more shapes Mohini could have made.
Solution:

1. Yes, this shape is also a closed shape and it has 6 sides.

2. No, this shape is not the same as the one made by Rohini, even though both have 6 sides.

3. Yes, these shapes are different because the angles between their sides are different. Even with the same number of sides, changing the angles changes the shape.

4. Mohini could have made other shapes with 6 sides by changing the angles. Here are two examples of different shapes she could have made:

(Imagine two different 6-sided polygons drawn here, distinct from Rohini's and Mohini's initial shapes, perhaps with sharper or wider angles.)

Question 3

Look at the angles marked in these shapes. Can you see the difference?

(Imagine three figures here showing shapes with different angles marked.)

Solution:

Yes, the angles marked in these figures are different. The size and measure of the angles are what make these shapes look distinct from each other, even if they might have the same number of sides.

NCERT Textbook Page 17-18

Practice Time

Question 4

Look at the shape and answer: The angle marked in—colour is the biggest angle.

(Imagine a shape with different colored angles marked, one of which is the biggest.)

Solution:

The angle marked in black is the biggest angle in the given shape.

Question 5

Are the angles marked with yellow equal?

Solution:

Yes, the angles marked with yellow are equal to each other.

Question 6

Are the angles marked with green equal?

Solution:

Yes, the angles marked with green are equal to each other.

Question 7

Are the angles marked with blue equal?

Solution:

Yes, the angles marked with blue are equal to each other.

Question 8

Four different angles are marked in four colours. Can you find other angles which are the same as the one marked in red? Mark them in red. Do this for other colours.

(Imagine a figure with angles marked in red, yellow, green, and black. The task is to find and mark other angles that are equal to these.)

Solution:

By observing the figure, we can identify other angles that are equal to the ones marked. The angle marked in yellow is the same as the angle marked in red. All the angles within the hexagon are equal to the angle marked in green. Similarly, all the angles within the octagon are equal to the angle marked in black.

Common mistakes

  • Confusing open and closed shapes.
  • Incorrectly counting the sides of a polygon.
  • Not recognizing that different angles create different shapes, even with the same number of sides.
  • Difficulty in visually comparing angles of different sizes.

Revision tips

  • Practice drawing various closed shapes with 6 sides and observe how changing angles alters them.
  • Use colored pencils to mark and compare angles in different shapes as shown in the exercises.
  • Focus on the visual differences in angles when comparing shapes that have the same number of sides.
  • Review the definitions of open and closed shapes before attempting the exercises.

Practice MCQs

Q1. Which of the following is a closed shape?

Q2. If a shape has 6 sides and all its sides are connected, what kind of shape is it?

Q3. What determines the specific form or appearance of a shape, even if it has the same number of sides as another?

Q4. In the given shapes, if angles marked in yellow are equal, what does this imply?

Q5. Rohini made a shape with 6 sides. Mohini made a different shape also with 6 sides. What could be the reason for the difference?

Frequently asked questions

What is the main difference between an open and a closed shape in Class 5 Maths?

An open shape has ends that do not meet, while a closed shape has all its sides connected to form a complete boundary without any gaps.

How do angles affect a shape?

Angles determine the specific form and appearance of a shape. Even if two shapes have the same number of sides, different angles will make them look different.

What does it mean if angles are marked with the same color in the NCERT exercises?

If angles are marked with the same color, it indicates that these angles have equal measures.

Are these NCERT Solutions for Class 5 Maths helpful for exams?

Yes, these solutions provide clear explanations and step-by-step methods for understanding shapes and angles, which are crucial concepts for Class 5 Mathematics exams.

How can I use these solutions to learn about shapes and angles?

You can use these solutions to understand the concepts of open/closed shapes, count sides, and compare angles by following the rewritten explanations and examples provided for each question.

Important links

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