Types of Angles Practice Worksheets with Solutions for Grade 4

Complete practice worksheets covering acute, right, obtuse, straight, and reflex angles with 5 detailed exercises and visual diagrams.

Worksheet Solutions: Exercises 1 to 3
1 Angle Classification Worksheet
Exercise 1
Classify each angle in the following list as acute, right, obtuse, straight, or reflex: 20°, 90°, 110°, 180°, 270°, 45°, 135°, 200°, 60°, 150°
Definitions:

Acute angle: 0° < angle < 90°, Right angle: angle = 90°, Obtuse angle: 90° < angle < 180°

Straight angle: angle = 180°, Reflex angle: 180° < angle < 360°

Classification method:
  1. Review angle definitions: Know the range for each angle type
  2. Compare each angle: Compare to key values: 0°, 90°, 180°, 270°, 360°
  3. Determine the range: Identify which category the angle falls into
  4. Assign type: Give the appropriate angle classification
20°
Acute
90°
Right
110°
Obtuse
180°
Straight
Angles
20°, 90°, 110°, 180°, 270°, 45°, 135°, 200°, 60°, 150°
Types
A, R, O, S, Re, A, O, Re, A, O
Result
See below
Step 1: Analyze 20°

0° < 20° < 90° → Acute angle

Step 2: Analyze 90°

90° = 90° → Right angle

Step 3: Analyze 110°

90° < 110° < 180° → Obtuse angle

Step 4: Continue for all angles

180° = 180° → Straight angle

270°: 180° < 270° < 360° → Reflex angle

45°: 0° < 45° < 90° → Acute angle

135°: 90° < 135° < 180° → Obtuse angle

200°: 180° < 200° < 360° → Reflex angle

60°: 0° < 60° < 90° → Acute angle

150°: 90° < 150° < 180° → Obtuse angle

A=20°,45°,60°; R=90°; O=110°,135°,150°; S=180°; Re=270°,200°
Final answer:

20°=Acute, 90°=Right, 110°=Obtuse, 180°=Straight, 270°=Reflex, 45°=Acute, 135°=Obtuse, 200°=Reflex, 60°=Acute, 150°=Obtuse

Applied rules:

• Acute: 0° < angle < 90°

• Right: angle = 90°

• Obtuse: 90° < angle < 180°

• Straight: angle = 180°

• Reflex: 180° < angle < 360°

2 Triangle Angle Worksheet
Exercise 2
A triangle has angles measuring 50°, 60°, and 70°. What type of triangle is this based on its angles? What can you say about the sides?
Key definitions:

Acute triangle: All three angles are acute (less than 90°)

Equilateral triangle: All three sides are equal

Scalene triangle: All three sides are different

50° 60° 70°
Angles
50°, 60°, 70°
All acute?
Yes
Type
Acute triangle
Step 1: Analyze all angles

50°: 0° < 50° < 90° → acute

60°: 0° < 60° < 90° → acute

70°: 0° < 70° < 90° → acute

Step 2: Classify the triangle

Since all three angles are acute, this is an acute triangle

Step 3: Analyze the sides

Since all angles are different, all sides must also be different

This is a scalene triangle

Step 4: Verify the sum

50° + 60° + 70° = 180° ✓

Step 5: Conclusion

This is an acute scalene triangle

Acute scalene triangle
Final answer:

This is an acute triangle (all angles less than 90°) and a scalene triangle (all sides different)

Applied rules:

• Acute triangle: All angles less than 90°

• Triangle sum: All three angles sum to 180°

• Side-angle relationship: Different angles → different sides

3 Quadrilateral Angle Worksheet
Exercise 3
A quadrilateral has angles measuring 90°, 90°, 90°, and 90°. What type of quadrilateral is this? What can you say about its sides?
Key information:

Rectangle: A quadrilateral with all angles equal to 90°

Square: A rectangle with all sides equal

Quadrilateral sum: All four angles sum to 360°

90° 90° 90° 90°
Angles
90°, 90°, 90°, 90°
All equal?
Yes
Type
Rectangle
Step 1: Analyze the angles

All four angles measure 90°

Step 2: Apply quadrilateral classification

A quadrilateral with all angles equal to 90° is a rectangle

Step 3: Consider the sides

Based on angle information alone, sides could be equal or unequal

If all sides are equal, it would be a square

Step 4: Verify the sum

90° + 90° + 90° + 90° = 360° ✓

Step 5: Conclusion

This is a rectangle (or possibly a square if sides are equal)

Rectangle (possibly square)
Final answer:

This is a rectangle with all right angles. It could be a square if all sides are equal.

Applied rules:

• Rectangle: All angles equal to 90°

• Square: Rectangle with all sides equal

• Quadrilateral sum: All angles sum to 360°

Angle Classification Worksheet Templates
A + R + O + S + Re = Complete Understanding
Angle Learning Formula
Acute Angle
0° < angle < 90°
Less than 90°
Right Angle
angle = 90°
Exactly 90°
Obtuse Angle
90° < angle < 180°
Between 90° and 180°
Straight Angle
angle = 180°
Exactly 180°
Reflex Angle
180° < angle < 360°
Between 180° and 360°
Worksheet Template: Angle Identification
Instructions: For each angle, write whether it is acute, right, obtuse, straight, or reflex.
Example: 45° → Acute, 90° → Right, 120° → Obtuse
Practice: 30°, 180°, 270°, 89°, 91°, 179°, 181°
Worksheet Template: Triangle Classification
Rule: Classify triangles based on their angles:
• All acute → Acute triangle
• One right → Right triangle
• One obtuse → Obtuse triangle
Worksheet Template: Quadrilateral Analysis
Key: Sum of all angles = 360°
• All 90° → Rectangle/Square
• Opposite angles equal → Parallelogram/Rhombus
Worksheet Solutions: Exercises 4 to 5
4 Clock Angle Worksheet
Exercise 4
At what time(s) do the clock hands form an acute angle? An obtuse angle? A straight angle? Explain your reasoning.
Clock mathematics:

Each hour represents 30° (360° ÷ 12 = 30° per hour)

Each minute represents 6° (360° ÷ 60 = 6° per minute)

90°
3:00 (Right)
120°
4:00 (Obtuse)
180°
6:00 (Straight)
Acute
0°-90°
Obtuse
90°-180°
Straight
180°
Step 1: Calculate angles at different times

At 1:00: Angle ≈ 30° (Acute)

At 2:00: Angle ≈ 60° (Acute)

At 3:00: Angle = 90° (Right)

At 4:00: Angle ≈ 120° (Obtuse)

Step 2: Identify acute angle times

Acute angles occur when the angle is between 0° and 90°

Examples: 1:00, 2:00, 10:00, 11:00

Step 3: Identify obtuse angle times

Obtuse angles occur when the angle is between 90° and 180°

Examples: 4:00, 5:00, 7:00, 8:00

Step 4: Identify straight angle times

Straight angles occur when the angle is exactly 180°

Examples: 6:00 (and 6:00 PM)

Step 5: Reasoning explanation

As the hour hand moves, the angle between hands changes continuously

At 6:00, hands are exactly opposite each other forming 180°

Acute: 1-2, 10-11; Obtuse: 4-5, 7-8; Straight: 6:00
Final answer:

Acute angles: Approximately 1:00, 2:00, 10:00, 11:00

Obtuse angles: Approximately 4:00, 5:00, 7:00, 8:00

Straight angle: 6:00 (hands opposite each other)

Applied rules:

• Clock angles: Each hour represents 30°

• Angle ranges: Apply angle type definitions

• Continuous change: Angle changes as hands move

5 Polygon Angle Worksheet
Exercise 5
A regular pentagon has five equal angles. What type of angles are these? Calculate the measure of each angle and explain why they are this type.
Key information:

Regular polygon: All sides and angles are equal

Angle sum formula: (n-2) × 180° where n is number of sides

108° 108° 108° 108° 108°
Pentagon
n = 5
Sum
(5-2)×180° = 540°
Each angle
540°÷5 = 108°
Step 1: Apply the angle sum formula

For any polygon with n sides: Sum = (n-2) × 180°

For pentagon (n=5): Sum = (5-2) × 180° = 3 × 180° = 540°

Step 2: Calculate each angle

Since all angles are equal in a regular pentagon:

Each angle = 540° ÷ 5 = 108°

Step 3: Classify the angle type

Since 90° < 108° < 180°, each angle is obtuse

Step 4: Verify the classification

108° is greater than 90° but less than 180° → obtuse ✓

Step 5: Conclusion

A regular pentagon has 5 equal obtuse angles of 108° each

Each angle = 108° → Obtuse angles
Final answer:

Each angle in a regular pentagon measures 108°, making them all obtuse angles

Applied rules:

• Polygon angle sum: (n-2) × 180°

• Regular polygon: All angles equal

• Angle classification: Based on measure range

Complete Angle Types Worksheet Guide
A < R < O < S < Re
Angle Size Order
Key definitions:

Acute angle: An angle that measures greater than 0° but less than 90° (0° < angle < 90°)

Right angle: An angle that measures exactly 90° (angle = 90°)

Obtuse angle: An angle that measures greater than 90° but less than 180° (90° < angle < 180°)

Straight angle: An angle that measures exactly 180° (angle = 180°)

Reflex angle: An angle that measures greater than 180° but less than 360° (180° < angle < 360°)

Angle classification method:
  1. Measure the angle: Use a protractor to find the exact degree measure
  2. Compare to reference angles: Compare to 0°, 90°, 180°, 270°, 360°
  3. Identify the range: Determine which category the angle falls into
  4. Classify: Assign the appropriate angle type
Tip 1: Remember "A Cute" for acute angles - they're small and cute, less than 90°.
Tip 2: "Right on!" - right angles are exactly 90°, just right!
Tip 3: "Obvious" - obtuse angles are obvious because they're larger than 90°.
Tip 4: "Straight line" - straight angles form a perfectly flat line at 180°.
Common errors: Confusing acute with obtuse, forgetting that right angles are exactly 90°, misclassifying angles near boundaries.
Memory aid: "A ROSR" - Acute (0-90), Right (90), Obtuse (90-180), Straight (180), Reflex (180-360).
Essential facts to remember:

• Acute: 0° < angle < 90°

• Right: angle = 90°

• Obtuse: 90° < angle < 180°

• Straight: angle = 180°

• Reflex: 180° < angle < 360°

• Classification: Each angle fits into exactly one category

Angle Types Practice Chart
Acute
45°
Less than 90°
Right
90°
Exactly 90°
Obtuse
135°
Greater than 90°
Straight
180°
Exactly 180°

Angle Types Summary: Remember the characteristics of each angle type:

  • Acute angles are "sharp" and narrow, less than 90°
  • Right angles form perfect L-shapes at exactly 90°
  • Obtuse angles are "wide" and open, greater than 90°
  • Straight angles form a completely flat line at 180°
  • Reflex angles are even wider, greater than 180° but less than 360°

Use this chart to practice identifying and classifying angles!

Questions & Answers

Question: How do I remember the difference between acute and obtuse angles? They both sound similar.

Answer: Great question! Here are some helpful memory tricks:

  1. Acute = "A" for "All small": Think of "acute" as "a-cute" like something small and cute. Acute angles are small (less than 90°).
  2. Obtuse = "Obvious": Think of "obtuse" as "obvious" - these angles are obviously big and wide (greater than 90°).
  3. Size comparison: Acute angles are smaller than a right angle, obtuse angles are bigger than a right angle.

Another way to remember: "A" comes before "O" in the alphabet, just like acute angles (smaller) come before obtuse angles (larger) when comparing to 90°!

Practice by looking around for acute angles (like the tip of a slice of pizza) and obtuse angles (like the opening of a wide-open book).

Question: What happens if I measure an angle and get exactly 90°? Is it acute or right?

Answer: If an angle measures exactly 90°, it is definitely a right angle, not an acute angle!

Here's the important distinction:

  • Acute angles: Measure LESS than 90° (0° < acute angle < 90°)
  • Right angles: Measure EXACTLY 90° (right angle = 90°)

Think of it like this: acute angles are "less than" 90°, so they can't include 90° itself. Only right angles can equal exactly 90°.

This is why we have separate categories - each type has a specific range with exact boundaries. 90° is the boundary between acute and obtuse, but it belongs to the right angle category.

Remember: "Right on the dot!" - exactly 90° makes it a right angle.

Question: Can an angle be both acute and obtuse at the same time?

Answer: No, an angle cannot be both acute and obtuse at the same time! This would be impossible.

Think about the definitions:

  • Acute angle: Measures between 0° and 90° (less than 90°)
  • Obtuse angle: Measures between 90° and 180° (greater than 90°)

These ranges don't overlap at all! An angle can only have one measurement, so it can only fall into one category.

It's like asking if someone can be both shorter than 5 feet AND taller than 5 feet at the same time - it's impossible because these conditions contradict each other.

Every angle fits into exactly one category: acute, right, obtuse, straight, or reflex. This is called being "mutually exclusive" - the categories don't overlap.

Question: What's the difference between a straight angle and a reflex angle? They both seem pretty big.

Answer: Great observation! Both are large angles, but they differ in their exact measurements:

  • Straight angle: Measures exactly 180° - this is a perfectly flat line
  • Reflex angle: Measures greater than 180° but less than 360° - this is larger than a straight line but less than a full circle

Think of it this way:

A straight angle is like folding a piece of paper flat - you get a 180° angle.

A reflex angle is like continuing to fold past flat - now you have more than 180° but less than going all the way around (360°).

If you imagine a clock, a straight angle would be like the hands at 6 o'clock (180°), while a reflex angle would be like the hands at 8 o'clock if you measured the larger angle between them (240°).

The key is that reflex angles are "bigger than straight" but "smaller than full circle."

Question: How can I check if I've classified an angle correctly?

Answer: Here's a systematic way to verify your angle classification:

  1. Measure accurately: Use a protractor to get the precise angle measurement
  2. Compare to boundaries: Check where your measurement falls in relation to 90°, 180°, etc.
  3. Use the range definitions: Make sure your angle fits within the correct range for that type
  4. Visual check: Does your angle look like it should be acute (sharp), right (square corner), or obtuse (wide)?

Quick verification method:

  • Acute: Should look "pointy" and measure less than 90°
  • Right: Should look like a perfect corner and measure exactly 90°
  • Obtuse: Should look "wide" and measure more than 90° but less than 180°
  • Straight: Should look like a flat line and measure exactly 180°
  • Reflex: Should look like more than a flat line but less than a circle

Always double-check your protractor reading and make sure you're measuring from the correct starting point!