Shapes and Angles Class 5 Notes: CBSE Maths Chapter 2 (Math-Magic)

Closed-Sided Figure

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

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.

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

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

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.

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. 

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.

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.

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. 

1. 20 degrees

2. 45 degrees

3. 80 degrees 

4. 180 degrees

B. 

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

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.

5 Important Topics of Class 5 Maths Chapter 2 Shapes and Angles

Importance of Maths Chapter 2 Shapes and Angles Class 5 Notes

• Revision notes help us quickly understand and remember key concepts before exams.

• They save time by focusing on essential information and skipping unnecessary details.

• These notes simplify complex topics, making them easier to understand and use.

• They provide practical examples that show how theoretical knowledge is used in real-life situations.

• They increase confidence by clearly understanding what to expect in exams.

• The class 5 notes of Chapter 2 Shapes and Angles cover fundamental concepts of shapes and angles.

Tips for Learning the Class 5 Maths Chapter 2 Shapes and Angles

• Learn to draw different shapes like triangles, squares, and circles to understand their properties better.

• Learn how to use a protractor to measure angles. It’s a fun tool that helps you see how big or small an angle is!

• Learn to find shapes and angles in your surroundings—like windows, doors, and books—to see how they are used in real life.

• Relate to real-world examples like surroundings to see their shapes and improve your understanding.

Conclusion

These notes on Class 5 Maths Chapter 2, "Shapes and Angles," cover the important ideas you need to know. You’ve learned about different shapes like triangles and squares, how to measure angles, and how shapes can be symmetrical. Revisiting these notes and practising these concepts will help you understand how shapes and angles work and make it easier to solve problems. Keep practising and looking for shapes and angles around you to become even better at geometry!

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