Solved Exercises on Types of Angles and Their Names in Grade 4

Master types of angles and their names: acute, right, obtuse, straight, and reflex angles through these 5 detailed exercises with visual diagrams.

Solution: Exercises 1 to 3
1 Angle Name Identification
Exercise 1
Name the type of angle for each measure: 30°, 90°, 120°, 180°, 270°, 45°, 135°, 200°
Definitions:

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

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

Method:
  1. Compare each angle to the key values: 0°, 90°, 180°, 270°, 360°
  2. Determine which range the angle falls into
  3. Assign the appropriate name based on the range
  4. Verify the classification is correct
30°
Acute
90°
Right
120°
Obtuse
180°
Straight
Angles
30°, 90°, 120°, 180°, 270°, 45°, 135°, 200°
Names
A, R, O, S, Re, A, O, Re
Result
See below
Step 1: Analyze 30°

0° < 30° < 90° → Acute angle

Step 2: Analyze 90°

90° = 90° → Right angle

Step 3: Analyze 120°

90° < 120° < 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

30°=Acute, 90°=Right, 120°=Obtuse, 180°=Straight, 270°=Reflex, 45°=Acute, 135°=Obtuse, 200°=Reflex
Final answer:

30°=Acute, 90°=Right, 120°=Obtuse, 180°=Straight, 270°=Reflex, 45°=Acute, 135°=Obtuse, 200°=Reflex

Applied rules:

• Acute: 0° < angle < 90°

• Right: angle = 90°

• Obtuse: 90° < angle < 180°

• Straight: angle = 180°

• Reflex: 180° < angle < 360°

2 Drawing Angles with Names
Exercise 2
Draw an acute angle that measures 60° and label it with its name. Then draw an obtuse angle that measures 120° and label it with its name.
Definitions:

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

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

60°
Acute Angle
120°
Obtuse Angle
Draw
60°
Classify
Acute
Draw
120°
Step 1: Draw acute angle (60°)

Draw two rays forming a 60° angle at the vertex

Step 2: Verify acute classification

Since 0° < 60° < 90°, it's an acute angle

Step 3: Draw obtuse angle (120°)

Draw two rays forming a 120° angle at the vertex

Step 4: Verify obtuse classification

Since 90° < 120° < 180°, it's an obtuse angle

Step 5: Label both angles

Mark each angle with its measurement and name

Acute (60°) and Obtuse (120°) angles drawn and labeled
Final answer:

Drew acute angle (60°) and obtuse angle (120°) with proper labels

Applied rules:

• Acute angle: Measures between 0° and 90°

• Obtuse angle: Measures between 90° and 180°

• Measurement: Use protractor for accuracy

3 Angle Name Matching
Exercise 3
Match each angle measure with its correct name: 45°, 90°, 135°, 180°, 270°. Then explain why each name is correct.
Key information:

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

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

45°
Acute
90°
Right
135°
Obtuse
180°
Straight
Given
45°, 90°, 135°, 180°, 270°
Match
A, R, O, S, Re
Verify
Correct ranges
Step 1: Match 45°

45° is between 0° and 90° → Acute angle

Step 2: Match 90°

90° equals exactly 90° → Right angle

Step 3: Match 135°

135° is between 90° and 180° → Obtuse angle

Step 4: Match 180°

180° equals exactly 180° → Straight angle

Step 5: Match 270°

270° is between 180° and 360° → Reflex angle

45°=Acute, 90°=Right, 135°=Obtuse, 180°=Straight, 270°=Reflex
Final answer:

45°=Acute, 90°=Right, 135°=Obtuse, 180°=Straight, 270°=Reflex

Applied rules:

• Acute: 0° < angle < 90°

• Right: angle = 90°

• Obtuse: 90° < angle < 180°

• Straight: angle = 180°

• Reflex: 180° < angle < 360°

Angle Names and Their Ranges
A < R < O < S < Re
Angle Size Order
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°
Acute Angle
Small angles
Less than 90°
Right Angle
Square corners
Exactly 90°
Obtuse Angle
Wide angles
Greater than 90°
Straight Angle
Flat line
Exactly 180°
Solution: Exercises 4 to 5
4 Angle Name Problem Solving
Exercise 4
If angle A is half of a right angle and angle B is twice the size of angle A, what are the names of angles A and B? Show your work.
Key information:

Right angle = 90°, Half of right angle = 90° ÷ 2 = 45°

45°
Angle A (45°)
90°
Angle B (90°)
Calculate A
A = 90° ÷ 2 = 45°
Calculate B
B = 2 × A = 90°
Name
A=Acute, B=Right
Step 1: Calculate angle A

Angle A = ½ × right angle = ½ × 90° = 45°

Since 0° < 45° < 90°, angle A is acute

Step 2: Calculate angle B

Angle B = 2 × angle A = 2 × 45° = 90°

Step 3: Name angle B

Since angle B = 90°, it is a right angle

Step 4: Verify the answer

Angle A (45°) is acute ✓, Angle B (90°) is right ✓

A=Acute (45°), B=Right (90°)
Final answer:

Angle A is acute (45°) and Angle B is right (90°)

Applied rules:

• Right angle: Measures exactly 90°

• Arithmetic: Division and multiplication of angle measures

• Classification: Based on final angle measure

5 Critical Thinking
Exercise 5
Explain why it's impossible for an angle to have more than one name. Give examples of what angles would be acute and what would be obtuse.
Key information:

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

45°
Acute (45°)
135°
Obtuse (135°)
Ranges
A: 0°-90°, O: 90°-180°
Overlap
No intersection
Conclusion
Mutually exclusive
Step 1: Define acute angles

Acute angles measure between 0° and 90° (not including 0° and 90°)

Examples: 30°, 45°, 60°, 89°

Step 2: Define obtuse angles

Obtuse angles measure between 90° and 180° (not including 90° and 180°)

Examples: 91°, 120°, 150°, 179°

Step 3: Analyze the ranges

Acute range: 0° < angle < 90°

Obtuse range: 90° < angle < 180°

There is no overlap between these ranges

Step 4: Conclusion

An angle cannot simultaneously be less than 90° AND greater than 90°

These conditions contradict each other, so no angle can have multiple names

Impossible due to contradictory ranges
Final answer:

It's impossible because acute angles are less than 90° while obtuse angles are greater than 90°. Examples of acute: 30°, 45°, 60°. Examples of obtuse: 120°, 135°, 150°.

Applied rules:

• Mutual exclusivity: Categories don't overlap

• Logical contradiction: Can't be both less and greater than 90°

• Range analysis: Examine boundaries and overlaps

Detailed Summary: Types of Angles and Their Names
Acute < Right < Obtuse < Straight < Reflex
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 naming 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. Name: Assign the appropriate angle name
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

Visual Angle Name Guide
Acute
45°
Less than 90°
Right
90°
Exactly 90°
Obtuse
135°
Greater than 90°
Straight
180°
Exactly 180°

Angle Names Summary: Remember the characteristics of each angle name:

  • 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°

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 have more than one name? Like could it be both acute and obtuse?

Answer: No, an angle cannot have more than one name! 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 named an angle correctly?

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

  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!