Solved Exercises on Types of Angles and Degrees in Grade 4

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

Solution: Exercises 1 to 3
1 Acute Angle Recognition
Exercise 1
Identify which of these angles are acute: 25°, 90°, 120°, 45°, 89°, 91°, 60°, 100°
Definition:

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

Method:
  1. Recall the definition of an acute angle
  2. Compare each given angle to 90°
  3. Select angles that are less than 90°
  4. Verify that the angle is greater than 0°
25°
Acute
45°
Acute
89°
Acute
60°
Acute
List
25°, 90°, 120°, 45°, 89°, 91°, 60°, 100°
Filter
0° < angle < 90°
Result
25°, 45°, 89°, 60°
Step 1: Understand the definition

An acute angle measures between 0° and 90°, not including 0° and 90°

Step 2: Compare each angle to 90°

25° < 90° ✓, 90° = 90° ✗, 120° > 90° ✗, 45° < 90° ✓

89° < 90° ✓, 91° > 90° ✗, 60° < 90° ✓, 100° > 90° ✗

Step 3: List the acute angles

Acute angles: 25°, 45°, 89°, 60°

Step 4: Verify each is greater than 0°

All listed angles are greater than 0° ✓

Acute angles: 25°, 45°, 89°, 60°
Final answer:

The acute angles are: 25°, 45°, 89°, 60°

Applied rules:

• Acute angle range: 0° < angle < 90°

• Comparison: Less than 90°

• Classification: Based on angle measure

2 Right Angle Identification
Exercise 2
Which angle measure represents a right angle? A) 45° B) 90° C) 135° D) 180°
Definition:

Right angle: An angle that measures exactly 90°

90°
Right Angle
Options
A) 45° B) 90° C) 135° D) 180°
Definition
Right = 90°
Answer
B) 90°
Step 1: Recall the definition

A right angle measures exactly 90°

Step 2: Compare each option

A) 45° ≠ 90° ✗, B) 90° = 90° ✓, C) 135° ≠ 90° ✗, D) 180° ≠ 90° ✗

Step 3: Select the correct answer

Only option B equals exactly 90°

Step 4: Confirm the answer

90° is the only angle that measures exactly 90°

Answer: B) 90°
Final answer:

Option B) 90° represents a right angle

Applied rules:

• Right angle: Measures exactly 90°

• Equality: Must equal 90°

• Exact value: Precisely 90°

3 Obtuse Angle Practice
Exercise 3
Name the type of angle that measures 145°. Draw the angle and explain your answer.
Definition:

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

145° Vertex
Given
145°
Range
90° < 145° < 180°
Type
Obtuse
Step 1: Understand the definition

An obtuse angle measures between 90° and 180°

Step 2: Compare to boundaries

Is 90° < 145° < 180°?

Yes: 90° < 145° ✓ and 145° < 180° ✓

Step 3: Verify the classification

145° is greater than 90° but less than 180°

Step 4: Conclusion

Since 145° fits the obtuse angle range, it is an obtuse angle

145° is an obtuse angle
Final answer:

The angle measuring 145° is an obtuse angle

Applied rules:

• Obtuse angle range: 90° < angle < 180°

• Comparison: Greater than 90°, less than 180°

• Classification: Based on angle measure

Angle Types and Degree Measures
0° < A < 90° < R < 180° < Re < 360°
Angle Type Sequence
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°
30°
Acute
90°
Right
135°
Obtuse
180°
Straight
270°
Reflex
360°
Full
Solution: Exercises 4 to 5
4 Straight and Reflex Angles
Exercise 4
Classify these angles: 180°, 270°, 300°, 45°, 90°. Explain the differences between straight and reflex angles.
Definitions:

Straight angle: An angle that measures exactly 180° (forms a straight line)

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

180°
Straight
270°
Reflex
Given
180°, 270°, 300°, 45°, 90°
Classify
Str, Ref, Ref, Ac, R
Types
1 str, 2 ref, 1 ac, 1 r
Step 1: Analyze 180°

180° = exactly 180° → straight angle

Step 2: Analyze 270°

180° < 270° < 360° → reflex angle

Step 3: Analyze 300°

180° < 300° < 360° → reflex angle

Step 4: Analyze 45°

0° < 45° < 90° → acute angle

Step 5: Analyze 90°

90° = exactly 90° → right angle

180°=straight, 270°&300°=reflex, 45°=acute, 90°=right
Final answer:

180° is a straight angle, 270° and 300° are reflex angles, 45° is an acute angle, and 90° is a right angle

Applied rules:

• Straight angle: Measures exactly 180°

• Reflex angle: Measures between 180° and 360°

• Classification: Based on angle measure ranges

5 Angle Problem Solving
Exercise 5
If angle A is twice as large as a right angle, what type of angle is A? If angle B is half the size of a straight angle, what type of angle is B? If angle C is three times the size of a right angle, what type of angle is C?
Key information:

Right angle = 90°, Straight angle = 180°

180°
Angle A (180°)
90°
Angle B (90°)
Angle A
2 × 90° = 180°
Angle B
180° ÷ 2 = 90°
Angle C
3 × 90° = 270°
Step 1: Calculate angle A

Angle A = 2 × right angle = 2 × 90° = 180°

Since A = 180°, it is a straight angle

Step 2: Calculate angle B

Angle B = ½ × straight angle = ½ × 180° = 90°

Since B = 90°, it is a right angle

Step 3: Calculate angle C

Angle C = 3 × right angle = 3 × 90° = 270°

Since 180° < 270° < 360°, it is a reflex angle

Step 4: Verify classifications

Angle A (180°) → straight angle ✓

Angle B (90°) → right angle ✓

Angle C (270°) → reflex angle ✓

Step 5: Conclusion

Angle A is a straight angle, Angle B is a right angle, Angle C is a reflex angle

A=straight, B=right, C=reflex
Final answer:

Angle A is a straight angle (180°), Angle B is a right angle (90°), and Angle C is a reflex angle (270°)

Applied rules:

• Right angle: Measures 90°

• Straight angle: Measures 180°

• Arithmetic: Multiplication and division of angle measures

Detailed Summary: Types of Angles and Degrees
A < R < O < S < Re < F
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°)

Full rotation: An angle that measures exactly 360° (complete circle)

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

Visual Angle Comparison Guide
Acute
45°
0°-90°
Right
90°
Exactly 90°
Obtuse
135°
90°-180°
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°

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!