Angles (Grade 4)
When two straight lines meet at a point, they form an angle. We see angles everywhere — in the hands of a clock, in the corners of a book, and in the blades of a fan.
In Class 4, you will learn to identify different types of angles, compare them, and understand how angles are measured in degrees (°).
What is Angles - Class 4 Maths (Geometry)?
An angle is formed when two rays (arms) share a common starting point called the vertex.
The amount of turning from one arm to the other is the size of the angle. We measure angles in degrees, written with the symbol °.
A full turn equals 360°. A half turn equals 180°. A quarter turn equals 90°.
Angles (Grade 4) Formula
Full turn = 360° | Half turn = 180° | Quarter turn = 90°
To identify the type of an angle, compare it with 90°:
- If the angle is less than 90° → Acute
- If the angle is exactly 90° → Right angle
- If the angle is more than 90° but less than 180° → Obtuse
- If the angle is exactly 180° → Straight angle
Types and Properties
Angles are classified by their size:
| Type of Angle | Size | Looks Like |
|---|---|---|
| Acute Angle | Less than 90° | A slightly open book |
| Right Angle | Exactly 90° | Corner of a notebook |
| Obtuse Angle | Between 90° and 180° | A reclining chair |
| Straight Angle | Exactly 180° | A straight line |
| Reflex Angle | Between 180° and 360° | More than half a turn |
Right angle is the most common angle. The corner of every page, every door frame, and every tile has a right angle. A small square symbol (⊾) is drawn at the vertex to show a right angle.
Acute angles are smaller than a right angle. The hands of a clock at 1 o'clock form an acute angle.
Obtuse angles are larger than a right angle but smaller than a straight angle. The hands of a clock at 10 o'clock form an obtuse angle.
Solved Examples
Example 1: Example 1: Identify the angle type
Problem: Classify the angle that measures 45°.
Solution:
Step 1: Compare 45° with 90°.
Step 2: 45° is less than 90°.
Answer: 45° is an acute angle.
Example 2: Example 2: Identify the angle type
Problem: Classify the angle that measures 120°.
Solution:
Step 1: Compare 120° with 90° and 180°.
Step 2: 120° is greater than 90° but less than 180°.
Answer: 120° is an obtuse angle.
Example 3: Example 3: Right angle in real life
Problem: Aman opens his textbook and lays it flat on the desk. He folds one page straight up. What angle does the page make with the desk?
Solution:
Step 1: The desk is horizontal (flat). The page stands straight up (vertical).
Step 2: A horizontal line meeting a vertical line makes a 90° angle.
Answer: The page makes a right angle (90°) with the desk.
Example 4: Example 4: Counting right angles
Problem: How many right angles does a rectangle have?
Solution:
Step 1: A rectangle has 4 corners.
Step 2: Each corner of a rectangle is exactly 90°.
Answer: A rectangle has 4 right angles.
Example 5: Example 5: Clock angles
Problem: Priya looks at the clock. The time is 3 o'clock. What type of angle do the hour and minute hands form?
Solution:
Step 1: At 3 o'clock, the minute hand points to 12 and the hour hand points to 3.
Step 2: The hands cover 3 hours out of 12 on the clock face. That is 3/12 = 1/4 of a full turn.
Step 3: 1/4 of 360° = 90°.
Answer: The hands form a right angle (90°).
Example 6: Example 6: Clock angle — acute
Problem: What type of angle do the clock hands form at 2 o'clock?
Solution:
Step 1: At 2 o'clock, the hands cover 2 out of 12 hours = 2/12 = 1/6 of a full turn.
Step 2: 1/6 of 360° = 60°.
Step 3: 60° is less than 90°.
Answer: The hands form an acute angle (60°).
Example 7: Example 7: Turns and angles
Problem: Rahul faces North. He turns to face East. What angle did he turn through?
Solution:
Step 1: North to East is a quarter turn (clockwise).
Step 2: A quarter turn = 360° ÷ 4 = 90°.
Answer: Rahul turned through 90° (a right angle).
Example 8: Example 8: Straight angle
Problem: Meera faces North. She turns around to face South. What angle has she turned?
Solution:
Step 1: North to South is exactly a half turn.
Step 2: A half turn = 360° ÷ 2 = 180°.
Answer: Meera turned through a straight angle (180°).
Example 9: Example 9: Comparing angles
Problem: Arrange these angles from smallest to largest: 135°, 60°, 90°, 170°.
Solution:
Step 1: Compare all four values.
Step 2: 60° < 90° < 135° < 170°.
Answer: 60°, 90°, 135°, 170° (acute, right, obtuse, obtuse).
Example 10: Example 10: Identifying angle in a shape
Problem: A triangle has angles measuring 50°, 60°, and 70°. Classify each angle.
Solution:
Step 1: 50° < 90° → acute.
Step 2: 60° < 90° → acute.
Step 3: 70° < 90° → acute.
Answer: All three angles are acute angles. This is called an acute-angled triangle.
Real-World Applications
Angles appear everywhere in daily life:
- Clock hands form different angles at different times.
- Doors open at various angles — a fully open door is close to 180°.
- Scissors form an angle that changes as you open and close them.
- Slides in a park are set at an angle to the ground.
- Cricket bat and ball — the angle of the bat decides where the ball goes.
Key Points to Remember
- An angle is formed where two rays meet at a common point (vertex).
- Angles are measured in degrees (°).
- Acute angle: less than 90°.
- Right angle: exactly 90°. Marked with a small square.
- Obtuse angle: between 90° and 180°.
- Straight angle: exactly 180° — looks like a straight line.
- A full turn = 360°, half turn = 180°, quarter turn = 90°.
- Corners of squares and rectangles are always right angles.
Practice Problems
- Classify each angle: 30°, 90°, 145°, 180°, 72°.
- How many right angles are there in a square?
- At 6 o'clock, what type of angle do the clock hands form?
- Name two objects around you that have right angles.
- Kavi turns from facing North to facing West (clockwise). How many degrees has he turned? What type of angle is this?
- A triangle has one angle of 110°. What type of angle is it? Can the other two angles be obtuse? Why or why not?
- Arrange from largest to smallest: 88°, 179°, 90°, 5°, 120°.
Frequently Asked Questions
Q1. What is an angle in maths?
An angle is the amount of turn between two rays that share a common endpoint called the vertex. It is measured in degrees (°).
Q2. What are the four main types of angles?
The four main types are acute angle (less than 90°), right angle (exactly 90°), obtuse angle (between 90° and 180°), and straight angle (exactly 180°).
Q3. How do you identify a right angle?
A right angle measures exactly 90°. It looks like the corner of a book or a notebook. A small square symbol is drawn at the vertex to mark it.
Q4. What angle do clock hands make at 6 o'clock?
At 6 o'clock, the minute hand points to 12 and the hour hand to 6, forming a straight line. The angle is 180°, which is a straight angle.
Q5. Can a triangle have two obtuse angles?
No. The sum of all angles in a triangle is 180°. If two angles were each greater than 90°, their total would already exceed 180°, leaving no room for a third angle.
Q6. What is a reflex angle?
A reflex angle is an angle that measures more than 180° but less than 360°. It is the larger angle formed on the outside when two rays meet.
Q7. How many degrees are there in a full turn?
A full turn is 360°. This is why a circle is divided into 360 equal parts (degrees).
Q8. Where do we see angles in daily life?
Angles are seen in clock hands, open doors, scissor blades, slanting roofs, ramps, fan blades, and the letter V.
Q9. What is the difference between an angle and a corner?
A corner is the point where two edges of a shape meet. The angle is the measure of the opening at that corner, expressed in degrees.
