Types of Angles Answer Key with Detailed Solutions for Grade 4

Complete answer key for types of angles exercises with 5 detailed solutions covering acute, right, obtuse, straight, and reflex angles with visual diagrams.

Answer Key: Exercises 1 to 3
1 Angle Classification Answer Key
Exercise 1
Classify these angles: 25°, 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°

Solution method:
  1. Compare each angle to key values: 0°, 90°, 180°, 270°, 360°
  2. Determine which range the angle falls into
  3. Assign the appropriate classification
  4. Verify the classification is correct
25°
Acute
90°
Right
120°
Obtuse
180°
Straight
Given
25°, 90°, 120°, 180°, 270°, 45°, 135°, 200°
Classify
A, R, O, S, Re, A, O, Re
Answer
See below
Step 1: Classify 25°

0° < 25° < 90° → Acute angle

Step 2: Classify 90°

90° = 90° → Right angle

Step 3: Classify 120°

90° < 120° < 180° → Obtuse angle

Step 4: Classify 180°

180° = 180° → Straight angle

Step 5: Classify 270°

180° < 270° < 360° → Reflex angle

Step 6: Classify 45°

0° < 45° < 90° → Acute angle

Step 7: Classify 135°

90° < 135° < 180° → Obtuse angle

Step 8: Classify 200°

180° < 200° < 360° → Reflex angle

25°=A, 90°=R, 120°=O, 180°=S, 270°=Re, 45°=A, 135°=O, 200°=Re
Final answer:

25°=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 Triangle Classification Answer Key
Exercise 2
A triangle has angles measuring 60°, 60°, and 60°. What type of triangle is this? What type of angles does it have?
Key definitions:

Equilateral triangle: All sides equal, all angles equal (60° each)

Acute triangle: All angles less than 90°

60° 60° 60°
Angles
60°, 60°, 60°
All equal
✓ Equilateral
All acute
✓ Acute triangle
Step 1: Analyze the angles

All three angles measure 60°

Step 2: Classify by angles

Since 0° < 60° < 90°, all angles are acute

Step 3: Classify by sides

Since all angles are equal, all sides are equal (equilateral triangle)

Step 4: Verify the classification

60° + 60° + 60° = 180° ✓ (Triangle angle sum property)

Step 5: Conclusion

This is an equilateral triangle with all acute angles

Equilateral triangle with all acute angles
Final answer:

This is an equilateral triangle with all acute angles (each measuring 60°)

Applied rules:

• Equilateral triangle: All sides and angles equal

• Acute triangle: All angles less than 90°

• Triangle sum: All angles sum to 180°

3 Quadrilateral Classification Answer Key
Exercise 3
A quadrilateral has angles measuring 90°, 90°, 90°, and 90°. What type of quadrilateral could this be? Explain your reasoning.
Key information:

Quadrilateral: A polygon with 4 sides and 4 angles

Angle sum property: All four angles sum to 360°

90° 90° 90° 90°
Angles
90°, 90°, 90°, 90°
Sum
360°
Types
All right angles
Step 1: Verify the angle sum

90° + 90° + 90° + 90° = 360° ✓

Step 2: Analyze the angles

All four angles are right angles (90°)

Step 3: Consider possible shapes

A quadrilateral with all right angles could be a rectangle or a square

Step 4: Determine specific type

Without information about side lengths, it's a rectangle

If all sides are equal, it would be a square

Step 5: Conclusion

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

Rectangle (possibly square)
Final answer:

This could be a rectangle (or square if all sides are equal) since all four angles are right angles (90°)

Applied rules:

• Quadrilateral sum: All angles sum to 360°

• Rectangle: All angles are 90°

• Square: Rectangle with all sides equal

Complete Answer Key Summary
A + A = 180°, S₁ = S₂ → A₁ = A₂
Angle and Side Relationships
Exercise 1

Answer: 25°=A, 90°=R, 120°=O, 180°=S, 270°=Re, 45°=A, 135°=O, 200°=Re

Exercise 2

Answer: Equilateral triangle with all acute angles (60° each)

Exercise 3

Answer: Rectangle (all right angles)

Exercise 4

Answer: See detailed solution

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°
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°.
Answer Key: Exercises 4 to 5
4 Advanced Angle Classification
Exercise 4
If angle A is three times the size of a right angle and angle B is half the size of a straight angle, what type of angles are A and B?
Key information:

Right angle = 90°, Straight angle = 180°

270°
Angle A (270°)
90°
Angle B (90°)
Calculate A
A = 3 × 90° = 270°
Calculate B
B = 180° ÷ 2 = 90°
Classify
A=Reflex, B=Right
Step 1: Calculate angle A

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

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

Step 2: Calculate angle B

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

Since B = 90°, B is a right angle

Step 3: Verify classifications

Angle A (270°) → reflex angle ✓

Angle B (90°) → right angle ✓

A=Reflex (270°), B=Right (90°)
Final answer:

Angle A is a reflex angle (270°) and Angle B is a right angle (90°)

Applied rules:

• Right angle: Measures 90°

• Straight angle: Measures 180°

• Reflex angle: Measures between 180° and 360°

5 Comprehensive Review
Exercise 5
Create a table showing all angle types with their ranges, examples, and visual descriptions. Then explain why no angle can belong to more than one category.
Key concept:

Mutual exclusivity: Each angle fits into exactly one category

Angle Type Range Example Visual Description Acute 0° < angle < 90° 45° Narrow, sharp angle Right angle = 90° 90° Square corner Obtuse 90° < angle < 180° 120° Wide, open angle Straight angle = 180° 180° Flat line Reflex 180° < angle < 360° 270° More than flat line
Categories
5 distinct types
No overlap
Mutually exclusive
Reason
Contradictory ranges
Step 1: Examine acute range

Acute: 0° < angle < 90°

Step 2: Examine right condition

Right: angle = 90°

Step 3: Note non-overlapping ranges

Acute range doesn't include 90°, so an angle can't be both acute and right

Step 4: Apply to all categories

Each range has distinct boundaries with no overlap

Step 5: Conclusion

Since ranges don't overlap, each angle fits into exactly one category

Mutually exclusive categories
Final answer:

Angles are mutually exclusive - each angle fits into exactly one category because the ranges don't overlap

Applied rules:

• Mutual exclusivity: Categories don't overlap

• Distinct ranges: Each category has unique boundaries

• Logical contradiction: Can't satisfy multiple conditions

Complete Review: Types of Angles Answer Key
0° < A < R < O < S < Re < 360°
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 ROSR" - Acute (0-90), Right (90), Obtuse (90-180), Straight (180), Reflex (180-360).
Tip 2: "A Cute" - acute angles are small and cute, less than 90°.
Tip 3: "Right on!" - right angles are exactly 90°, just right!
Tip 4: "Obvious" - obtuse angles are obvious because they're larger than 90°.
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 Classification Guide
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°

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 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!