Shapes and Angles — Class 5 Mathematics (CBSE)
Based on the NCERT Math Magic Grade 5 textbook. Understand angles by looking at shapes around you, then solve the practice set without looking at the answers.
1. Why this chapter matters
Angles are everywhere — in the corners of your notebook, the hands of a clock, the slope of a roof, and the turn of a door. This chapter introduces students to the idea of angles as a measure of turn. Students learn to identify right angles, acute angles (smaller than a right angle), and obtuse angles (larger than a right angle). They also get a first look at measuring angles using a protractor and the degree symbol (°). This foundation will be used in higher classes for geometry, trigonometry, and design.
2. What is an angle?
An angle is formed when two lines meet at a common point. The common point is called the vertex. The two lines are called the arms of the angle.
We can also think of an angle as the amount of turn between two lines.
Types of angles
| Type of angle | Size | Description | Real-life example |
|---|---|---|---|
| Right angle | Exactly 90° | A quarter turn | Corner of a book, L-shape of a table |
| Acute angle | Less than 90° | Smaller than a right angle | Slant of a roof, a slice of pizza |
| Obtuse angle | More than 90° but less than 180° | Larger than a right angle | Open door, spread of a fan |
| Straight angle | Exactly 180° | A half turn | A straight line, pencil lying flat |
| Reflex angle | More than 180° | More than a straight line | Outside of an open book (not in Class 5 syllabus) |
| Complete angle | 360° | A full turn | One full rotation of a clock hand |
3. Identifying right angles around us
A right angle measures exactly 90 degrees. It looks like the letter 'L'.
Common places where we see right angles:
- Corners of a rectangular table
- Where the wall meets the floor
- The letter 'L' or 'T'
- The corner of a page in your notebook
Try this
Look around your classroom. Find five objects that have right angles. Make a list in your notebook.
4. Acute and obtuse angles
Acute angles are smaller than a right angle. If you open a book just a little, the angle between the pages is acute.
Obtuse angles are larger than a right angle but smaller than a straight angle. When you open a door wide, the angle between the door and the wall is obtuse.
| Angle type | Compared to a right angle | Degree range |
|---|---|---|
| Acute | Smaller | Between 0° and 90° |
| Right | Equal | Exactly 90° |
| Obtuse | Larger | Between 90° and 180° |
5. Measuring angles with a protractor
A protractor is a tool used to measure angles. It is usually a semi-circle marked with degrees from 0° to 180°.
Steps to measure an angle:
- Place the centre of the protractor on the vertex of the angle.
- Align the base line (0° line) of the protractor with one arm of the angle.
- Read the degree mark where the other arm crosses the protractor scale.
- Use the inner or outer scale carefully — start from zero on the correct side.
Steps to draw an angle of a given measure:
- Draw a base line (one arm of the angle).
- Place the protractor on the line with the centre at the vertex.
- Mark the required degree on the protractor scale.
- Remove the protractor and join the vertex to the marked point.
- Label the angle with its measure.
6. Angles in shapes
Every shape has angles at its corners (vertices).
| Shape | Number of sides | Number of angles | Type of angles |
|---|---|---|---|
| Triangle | 3 | 3 | Can be acute, right, or obtuse |
| Square | 4 | 4 | All right angles (90°) |
| Rectangle | 4 | 4 | All right angles (90°) |
| Pentagon | 5 | 5 | Usually obtuse in a regular pentagon |
| Hexagon | 6 | 6 | Usually obtuse in a regular hexagon |
Example: In a square, all four angles are right angles (90°). The total of all angles in a square = 90° x 4 = 360°.
7. Activity corner
Activity 1: Make an angle tester using two strips of cardboard joined with a paper fastener. Use it to compare angles around you. Find which are smaller than, equal to, or larger than a right angle.
Activity 2: Draw a triangle, a square, and a rectangle in your notebook. Mark each angle with a small arc and write 90° for right angles, 'A' for acute, or 'O' for obtuse.
Activity 3: Look at a clock. At 3 o'clock, the hands make a right angle. At 2 o'clock, what kind of angle do they make? Check with your angle tester.
8. Common mistakes
- Mistake: Thinking any slanted line makes an acute angle Fix: Compare the angle with a right angle. If it is visibly larger, it is obtuse, not acute.
- Mistake: Reading the wrong scale on the protractor Fix: Always start from 0° on the side where the base arm is aligned. Check whether the angle looks acute or obtuse to verify your reading.
- Mistake: Confusing the number of angles with the number of sides Fix: In any closed polygon, the number of angles equals the number of sides.
9. Key facts
- An angle is the amount of turn between two lines meeting at a point.
- A right angle = 90° (quarter turn).
- An acute angle is less than 90°.
- An obtuse angle is more than 90° but less than 180°.
- A protractor is used to measure angles in degrees.
- Every square and rectangle has four right angles.
- A triangle has three angles that together make 180°.
10. Self-test
- What is a right angle? How many degrees does it measure?
- Give two examples of acute angles from your daily life.
- Draw a triangle with one right angle. Label the right angle.
- Is an angle of 120° acute or obtuse? Explain why.
- How many right angles are there in a rectangle?
11. Answer key
-
What is a right angle? How many degrees does it measure? Answer: A right angle is a quarter turn. It measures exactly 90 degrees.
-
Give two examples of acute angles from your daily life. Answer: (Any two) The slant of a roof, a partially open book, the hands of a clock at 2 o'clock, a slice of pizza.
-
Draw a triangle with one right angle. Label the right angle. Answer: The triangle should have one corner marked with a small square symbol to show a right angle of 90°.
-
Is an angle of 120° acute or obtuse? Explain why. Answer: 120° is obtuse. It is larger than 90° (right angle) but smaller than 180° (straight angle).
-
How many right angles are there in a rectangle? Answer: A rectangle has four right angles (each 90°).
12. Quick revision
- An angle measures the turn between two meeting lines.
- Right angle = 90°, acute < 90°, obtuse > 90° (and < 180°).
- Use a protractor carefully — align the vertex and read from zero.
- In a square or rectangle, all angles are 90°.
- A triangle always has three angles that add up to 180°.
- Practise by comparing angles in objects around you.
