Right Angles
A right angle is one of the most important angles in geometry. It is the angle you see at the corner of a book, a door, a window, or a classroom wall. A right angle measures exactly 90 degrees (90°).
In Class 3, you learn to identify right angles, find them in everyday objects, and compare angles as smaller than, equal to, or greater than a right angle.
Recognising right angles helps you understand shapes, directions, and turns.
What is Right Angles - Class 3 Maths (Geometry (Grade 3))?
A right angle is an angle that measures exactly 90°. It looks like the corner of a square or rectangle.
The symbol for a right angle is a small square drawn at the corner:
┐
Right Angle = 90°
Angles compared to a right angle:
| Type | Compared to 90° | Example |
|---|---|---|
| Less than a right angle | Less than 90° | Acute angle (like a partly open book) |
| Right angle | Exactly 90° | Corner of a book |
| Greater than a right angle | More than 90° | Obtuse angle (like a wide-open door) |
Types and Properties
Where Do We See Right Angles?
1. In Shapes
- A square has 4 right angles.
- A rectangle has 4 right angles.
- A right-angled triangle has exactly 1 right angle.
2. In Everyday Objects
- Corner of a book, notebook, or sheet of paper
- Corner of a TV screen or computer monitor
- Corner of a door frame or window frame
- Where the wall meets the floor
- The letter L
3. In Turns
- A quarter turn (turning from facing North to facing East) is a right angle.
- A half turn = 2 right angles = 180°
- A full turn = 4 right angles = 360°
Solved Examples
Example 1: Example 1: Identifying a Right Angle
Question: Does the corner of a textbook form a right angle?
Think:
- A textbook has straight edges that meet at a corner
- The corner forms a perfect square corner
- It measures 90°
Answer: Yes, the corner of a textbook is a right angle.
Example 2: Example 2: Counting Right Angles in a Rectangle
Question: How many right angles does a rectangle have?
Think:
- A rectangle has 4 corners
- Each corner is 90°
Answer: A rectangle has 4 right angles.
Example 3: Example 3: Quarter Turn
Question: Aditi faces North. She makes a quarter turn to the right. Which direction does she face now?
Think:
- A quarter turn = 1 right angle = 90°
- Turning right from North → East
Answer: Aditi faces East.
Example 4: Example 4: More or Less Than a Right Angle
Question: A door is slightly open. Is the angle between the door and the wall more or less than a right angle?
Think:
- A slightly open door makes a small angle
- It is less than the corner of a book
Answer: The angle is less than a right angle (it is an acute angle).
Example 5: Example 5: Right Angles in the Letter L
Question: Does the letter L have a right angle?
Think:
- The letter L has a horizontal line meeting a vertical line
- They meet at 90°
Answer: Yes, the letter L has 1 right angle.
Example 6: Example 6: Half Turn
Question: How many right angles make a half turn?
Think:
- A half turn = 180°
- One right angle = 90°
- 180 ÷ 90 = 2
Answer: 2 right angles make a half turn.
Example 7: Example 7: Testing with Paper Corner
Question: How can you test if an angle is a right angle without a protractor?
Think:
- Take the corner of a piece of paper (which is already a right angle)
- Place the corner on the angle you want to test
- If it fits perfectly, the angle is a right angle
Answer: Use the corner of a paper to check. If the angle matches the paper corner exactly, it is a right angle.
Example 8: Example 8: Counting Right Angles in Shapes
Question: How many right angles does a triangle have at most?
Think:
- A triangle has 3 angles that add up to 180°
- If one angle is 90°, the other two add up to 90°
- A triangle can have at most 1 right angle
Answer: A triangle can have at most 1 right angle.
Example 9: Example 9: Full Turn
Question: Dev spins in a full circle. How many right angles did he turn through?
Think:
- Full turn = 360°
- 360 ÷ 90 = 4
Answer: Dev turned through 4 right angles.
Example 10: Example 10: Clock Hands
Question: At what time do the clock hands form a right angle?
Think:
- At 3:00, the minute hand is on 12 and the hour hand is on 3
- The angle between them = 90°
Answer: At 3 o'clock (and also at 9 o'clock), the clock hands form a right angle.
Real-World Applications
Where Are Right Angles Used?
- Buildings: Walls meet floors at right angles to keep buildings upright.
- Furniture: Tables, chairs, and bookshelves have right-angle corners.
- Road signs: Many traffic signs use right-angle corners.
- Maps: Grid lines on maps cross at right angles.
- Sports: The corners of a football field, cricket pitch boundary, and badminton court are right angles.
Key Points to Remember
- A right angle measures exactly 90°.
- It is shown by a small square symbol at the corner.
- A square and rectangle each have 4 right angles.
- An angle less than 90° is called an acute angle.
- An angle more than 90° is called an obtuse angle.
- A quarter turn = 1 right angle; a half turn = 2 right angles; a full turn = 4 right angles.
- You can test for a right angle using the corner of a piece of paper.
Practice Problems
- How many right angles does a square have?
- Name 3 objects in your classroom that have right angles.
- Ria faces South and makes 2 quarter turns to the right. Which direction does she face?
- Is the angle made by the hands of a clock at 6 o'clock a right angle? If not, what kind of angle is it?
- How many right angles make a full turn?
- Does the letter T have a right angle? Explain.
- A triangle has one right angle. The other two angles are equal. How many degrees is each?
Frequently Asked Questions
Q1. What is a right angle?
A right angle is an angle that measures exactly 90 degrees. It looks like the corner of a book or a square.
Q2. How do I identify a right angle?
Place the corner of a piece of paper on the angle. If the paper corner fits exactly, the angle is a right angle. You can also use a protractor to check if it measures 90°.
Q3. How many right angles does a square have?
A square has 4 right angles — one at each corner.
Q4. What is the difference between a right angle and an acute angle?
A right angle is exactly 90°. An acute angle is less than 90° — it is a smaller, sharper angle.
Q5. What is a quarter turn?
A quarter turn is one-fourth of a full rotation. It equals 90° or one right angle. Turning from North to East is a quarter turn.
Q6. Can a triangle have 2 right angles?
No. The three angles of a triangle add up to 180°. Two right angles alone would be 180°, leaving 0° for the third angle, which is not possible.
Q7. Where do we see right angles in daily life?
Right angles are everywhere — corners of books, doors, windows, tables, TV screens, floor tiles, and where walls meet the floor.
Q8. What is the symbol for a right angle?
A small square is drawn in the corner of the angle to show it is a right angle (90°).
Q9. How many degrees are in a full turn?
A full turn is 360°, which equals 4 right angles (4 × 90° = 360°).
