Introduction to Angles
An angle is formed when two lines or rays meet at a point. In Class 3, students learn what an angle is, how to spot angles around them, and how to tell the difference between a right angle, an angle less than a right angle, and an angle greater than a right angle.
Angles are found everywhere -- in the corners of a book, the hands of a clock, an open door, and even in the letter L.
What is Introduction to Angles - Class 3 Maths (Geometry)?
An angle is formed when two rays share a common starting point called the vertex. The two rays are called the arms of the angle.
Types of angles in Class 3:
- Right angle: Exactly like the corner of a book -- a square corner. It measures 90 degrees.
- Less than a right angle (acute): Smaller than a square corner.
- Greater than a right angle (obtuse): Wider than a square corner.
Types and Properties
How to check for a right angle:
- Take the corner of a sheet of paper or a book.
- Place it on the angle you want to check.
- If the corner fits exactly, the angle is a right angle.
- If there is a gap, the angle is greater than a right angle.
- If the corner overlaps, the angle is less than a right angle.
Solved Examples
Example 1: Identifying a Right Angle
Question: Look at the corner of your textbook. What type of angle is it?
Think:
- The corner of a textbook makes a perfect square corner.
- A square corner = right angle.
Answer: The corner of the textbook is a right angle.
Example 2: Angle Less Than a Right Angle
Question: The clock shows 2 o'clock. Is the angle between the hands less than, equal to, or greater than a right angle?
Think:
- At 2 o'clock, the minute hand is at 12 and the hour hand is at 2.
- The opening between them is smaller than a square corner.
Answer: The angle is less than a right angle.
Example 3: Angle Greater Than a Right Angle
Question: Priya opens her book wide so the two covers form a big V. Is this angle more or less than a right angle?
Think:
- The covers are opened wider than a square corner.
Answer: The angle is greater than a right angle.
Example 4: Counting Right Angles in a Shape
Question: How many right angles does a rectangle have?
Think:
- A rectangle has 4 corners.
- Each corner is a square corner = right angle.
Answer: A rectangle has 4 right angles.
Example 5: Angles in the Letter L
Question: What type of angle does the letter L make?
Think:
- The two lines in L meet at a square corner.
Answer: The letter L makes a right angle.
Example 6: Angles in a Triangle
Question: Dev draws a triangle. He checks each corner with the corner of his notebook. One corner fits exactly, and the other two are smaller. Describe the angles.
Think:
- One corner fits exactly → right angle
- Two corners are smaller → less than right angle
Answer: The triangle has 1 right angle and 2 angles less than a right angle.
Example 7: Angles Made by Clock Hands
Question: At 6 o'clock, what type of angle do the clock hands make?
Think:
- At 6 o'clock, the hands point in opposite directions (12 and 6).
- They make a straight line, which is two right angles.
Answer: The hands make a straight angle (greater than a right angle).
Example 8: Right Angles at 3 O'Clock
Question: At 3 o'clock, what angle do the clock hands make?
Think:
- The minute hand points to 12 and the hour hand points to 3.
- The opening is exactly a square corner.
Answer: At 3 o'clock, the hands make a right angle.
Example 9: Angles in Everyday Objects
Question: Meera opens her scissors slightly. Is the angle between the blades less than, equal to, or greater than a right angle?
Think:
- Scissors opened slightly make a small opening.
- This is less than a square corner.
Answer: The angle is less than a right angle.
Key Points to Remember
- An angle is formed when two rays meet at a point (the vertex).
- A right angle is exactly like a square corner (90 degrees).
- An angle less than a right angle is smaller than a square corner.
- An angle greater than a right angle is wider than a square corner.
- Use the corner of a book to test whether an angle is a right angle.
- A rectangle and a square each have 4 right angles.
- Clock hands at 3 o'clock make a right angle.
Practice Problems
- How many right angles are there in a square?
- At 12 o'clock, what angle do the clock hands make?
- Is the angle made by an open fan greater or less than a right angle?
- Name two objects in your home that have right angles.
- The letter T has how many right angles?
- Draw an angle that is less than a right angle.
- At 9 o'clock, what type of angle do the clock hands make?
Frequently Asked Questions
Q1. What is an angle?
An angle is formed when two rays meet at a common point called the vertex. The size of the angle depends on how wide the opening is between the two rays.
Q2. What is a right angle?
A right angle is exactly like the corner of a book or a square. It measures 90 degrees. A right angle is also called a square corner.
Q3. How can I check if an angle is a right angle?
Place the corner of a piece of paper or a book on the angle. If the corner fits perfectly, it is a right angle. If there is a gap or overlap, it is not.
Q4. What is the difference between acute and obtuse angles?
An acute angle is less than a right angle (less than 90 degrees). An obtuse angle is greater than a right angle (more than 90 degrees but less than 180 degrees).
Q5. How many right angles does a rectangle have?
A rectangle has 4 right angles, one at each corner.
Q6. What angle do clock hands make at 3 o'clock?
At 3 o'clock, the minute hand is at 12 and the hour hand is at 3. They form exactly one right angle (90 degrees).
Q7. Where do we find angles in everyday life?
Angles are found in corners of rooms, open doors, clock hands, scissors, letter shapes like L and T, and in triangles and other shapes.
Q8. What is a vertex?
The vertex is the point where two rays or lines meet to form an angle. It is the corner point of the angle.
Q9. Is introduction to angles in the NCERT Class 3 syllabus?
Yes. Introduction to angles is part of the Geometry chapter in NCERT Class 3 Maths. Students learn about right angles and compare angles to right angles.
