Shapes and Angles Class 5 Notes CBSE Maths Chapter 2 (Free PDF Download)

Closed-Sided Figure

•  A closed-form is an enclosed shape or figure whose line segments and/or curves are linked or meet in geometry.

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Image: Closed-Sided Figure

Open-Sided Figure: 

• An open shape is a shape or figure whose line segments and/or curves do not intersect in geometry. 

• They do not begin and terminate at the same location.

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Image: Open-Sided Figure

Polygons

• In geometry, a polygon is any closed curve made up of a series of line segments (sides). 

• Triangles (three sides), quadrilaterals (four sides), and pentagons(five sides) are the simplest polygons.

Shapes and Their Properties

Circle: 

• A circle is a round-shaped figure that has no corners or edges, it is a closed, two-dimensional curved shape. 

• The angles in a circle sum to 360 degrees.  A circle can be divided into smaller sections. The arc of a circle is a section that is named according to its angle.

Triangle: 

• A triangle is a closed, two-dimensional form with three straight sides in geometry.

• The sum of angles of a triangle is 180 degrees.

Quadrilateral: 

• A quadrilateral is a two-dimensional shape with four sides. All of the following 2D shapes are quadrilaterals: square, rectangle, and so on.

• The sum of angles of a quadrilateral is 360 degrees.

Pentagon: 

• A pentagon is a five-sided geometric form with five angles.

• The sum of angles of a pentagon is 540 degrees.

Hexagon:  

• A hexagon is a six-sided geometric form with six angles.

• The sum of angles of a hexagon is 720 degrees.

Heptagon: 

• A heptagon is a seven-sided geometric form with seven angles.

• The sum of angles of a heptagon is 900 degrees.

Octagon: 

• An octagon is an eight-sided geometric form with eight angles.

• The sum of angles of an octagon is 1080 degrees.

Nonagon:  

• A nonagon is a nine-sided geometric form with nine angles.

• The sum of angles of a nonagon is 1260 degrees.

Decagon:  

• A decagon is a ten-sided geometric form with ten angles.

• The sum of angles of a decagon is 1440 degrees.

Solved Examples of Shapes and their Properties

1. Select True or False: 

1. All cuboids can be considered a cube.

2. All cubes can be considered a cuboid.

3. Edges are absent in spherical shapes.

Answer: 

1. False

2. True

3. True

Types of Angles

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Image: Types of Angles

• Acute Angle: An acute angle is smaller than 90 degrees.

• Right Angle: A right angle is equal to 90 degrees.

• Obtuse Angle: An acute angle is greater than 90 degrees.

• Reflex Angle: A reflex angle is greater than 180 degrees.

• Straight Angle: A straight angle is equal to 180 degrees.

• Complete Angle: A complete angle is equal to 360 degrees.

Measuring Angles

• An angle measure in geometry is the measurement of the angle created by two rays or arms at a shared vertex. 

• Angles are measured using a simple geometric instrument such as a protractor. A protractor is more commonly used than a compass. 

• The sign '°' represents a degree. A circle spins 360°, and a degree is part of that rotation since it is split into 360 equal pieces. Angles with varying degrees include 30°, 45°, 90°, and so on. And is written as 30 degrees, 45 degrees, 90 degrees, and so on.

Angles Made by Clock at Different Time

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Image: Types of Angles made by a clock

• On a clock, we may see various angles based on their amplitude: acute, straight, obtuse, flat angles, and even complete angles.

• The full circumference of the clock is 360°. The distance between each number on the clock is similar to 30° (360/12) since the clock is divided into 12 pieces. 

• For example, the angle created between 1 o’clock and 2 o’clock is 30°.

Solved Example on Clocks and Angles

What is the angle made by the hour and the minute hands in the following images given below:

A.

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Answer: Angle made between 2 numbers in a clock= 30 degrees

Numbers between 8 and 1= 5

Therefore, total angle made is = 30×5 = 150 degrees

B. 

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Answer: Angle made between 2 numbers in a clock= 30 degrees

Numbers between 2 and 3= 1

Therefore, total angle made is = 30×1 = 30 degrees

C.

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Answer: Angle made between 2 numbers in a clock= 30 degrees

Numbers between 7 and 12= 5

Therefore, total angle made is = 30×5 = 150 degrees

D.

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Answer: Since the minute hand is just above the hour hand, that is from where it started therefore, the total angle covered is 360 degrees.

Practice Problems

1. Guess the angles in the following objects given below:

A. 

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1. 20 degrees

2. 45 degrees

3. 80 degrees 

4. 180 degrees

B. 

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1. 100 degrees

2. 360 degrees

3. 80 degrees 

4. 180 degrees

Ans: 

A) ii) 45 degrees

B) iv) 180 degrees

2. Fill in the blanks:

i) A pentagon has _______ sides.

ii) A circle has ________ sides.

iii) A square has _________ sides.

iv) An octagon has __________ sides.

Ans: 

1. 5

2. 0

3. 4

4. 8

Importance of CBSE Class 5 Maths Chapter 2 Shapes and Angles

• This chapter gives a glimpse of the internal angles of different shapes. Students will learn about shapes with more than four sides also in this chapter.

• They will also learn what an angle is and how to identify the bigger angles and smaller angles inside a geometric shape.

• The Shapes and Angles summary will also teach how one can make shapes using matchsticks to give a practical understanding to students.

• The students will also become aware of the different components of a geometry box and learn how to use them for drawing and measuring angles.

• On proceeding further, students will also learn about right angles. They will also identify which angles are smaller and bigger than the right angles.

• The pictorial questions will ask students to mark angles with colours and evaluate their logical reasoning skills.

Benefits of NCERT Class 5 Maths Shapes and Angles Notes and Worksheets

The subject experts at Vedantu have compiled a precise set of revision notes for Chapter 2. Students will enjoy studying the concepts of shapes and angles by following these simple explanations. The Class 5 Maths Shapes and Angles notes will help students in the following ways.

• Easier comprehension of the relationship between angles and sides of a geometric figure

• Understanding the features of a right angle

• Determining types of angles that are less than or greater than a right angle

• Learning how to guess the angles in the pictorial questions and answering them accurately by following the methods adopted by the subject experts

Practicing Maths Shapes and Angles Worksheets

Download the revision notes and worksheets compiled by Vedantu experts and find out how to solve the problems efficiently. Learn how the angles are measured in a geometric shape and clear your doubts on the sums of this chapter on your own. Download the free PDF and use them accordingly to score well in the exams.

Conclusion 

Class 5 CBSE Maths Chapter 2 - Shapes and Angles notes offer a comprehensive and engaging exploration of the world of geometry. These notes provide a clear understanding of various 2D and 3D shapes, their properties, and the concept of angles formed by these shapes. With well-structured explanations and illustrative examples, students can easily grasp the concepts and enhance their problem-solving skills. The free PDF download of the notes ensures easy accessibility to valuable study material, supporting students in their mathematical journey. Overall, these notes foster a strong foundation in geometry, empowering students to navigate the fascinating world of shapes and angles with confidence and enthusiasm.