Solved Exercises on Types of Angles in Grade 4

Master types of angles: acute, right, obtuse, and straight angles through these 3 detailed exercises with visual diagrams.

Solution: Exercises 1 to 3
1 Acute angle identification
Exercise 1
Identify the angle shown below. What type of angle is it?
45°
Definition:

Acute angle: An angle that measures less than 90°

Angle classification method:
  1. Measure the angle using a protractor (or given measurement)
  2. Compare the measurement to 90°
  3. If the angle is less than 90°, it's an acute angle
Angle measurement
45°
Comparison
45° < 90°
Classification
Acute angle
Step 1: Identify the angle measurement

The angle measures 45°

Step 2: Compare to 90°

Since 45° is less than 90°, the angle is smaller than a right angle

Step 3: Classify the angle

Any angle less than 90° is classified as an acute angle

The angle is an acute angle (45°)
Final answer:

This is an acute angle because it measures 45°, which is less than 90°

Applied rules:

• Acute angle rule: Any angle between 0° and 90° is acute

• Measurement: Use a protractor to determine the exact angle

• Classification: Compare the angle to 90° to determine its type

2 Right angle identification
Exercise 2
Identify the angle shown below. What type of angle is it?
90°
Definition:

Right angle: An angle that measures exactly 90°

Angle measurement
90°
Comparison
90° = 90°
Classification
Right angle
Step 1: Identify the angle measurement

The angle measures exactly 90°

Step 2: Compare to 90°

Since 90° equals 90°, the angle is exactly a right angle

Step 3: Classify the angle

Any angle that measures exactly 90° is classified as a right angle

The angle is a right angle (90°)
Final answer:

This is a right angle because it measures exactly 90°

Applied rules:

• Right angle rule: Any angle that measures exactly 90° is a right angle

• Shape: Right angles form a perfect L-shape

• Identification: Often marked with a small square in the corner

3 Obtuse angle identification
Exercise 3
Identify the angle shown below. What type of angle is it?
120°
Definition:

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

Angle measurement
120°
Comparison
90° < 120° < 180°
Classification
Obtuse angle
Step 1: Identify the angle measurement

The angle measures 120°

Step 2: Compare to 90° and 180°

Since 120° is greater than 90° but less than 180°, it falls between these values

Step 3: Classify the angle

Any angle greater than 90° but less than 180° is classified as an obtuse angle

The angle is an obtuse angle (120°)
Final answer:

This is an obtuse angle because it measures 120°, which is greater than 90° but less than 180°

Applied rules:

• Obtuse angle rule: Any angle between 90° and 180° is obtuse

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

• Visual: Wider than a right angle but not flat

Angle Classification Guide
Acute: 0° < θ < 90°
Acute Angle
Acute Angle
0° < θ < 90°
Less than a right angle
Right Angle
θ = 90°
Exactly 90 degrees
Obtuse Angle
90° < θ < 180°
Greater than right angle
Straight Angle
θ = 180°
Forms a straight line
Key concept: Angles are measured in degrees (°) and classified based on their size relative to 90° and 180°.
Memory tip: "Acute" sounds like "cute" - small and sharp. "Obtuse" means dull - wide and blunt.
Angle Types Visual Guide
Acute Angle (0° to 90°)
60° Examples: 30°, 45°, 60°, 89°

Acute angles are smaller than a right angle. They look "sharp" and narrow.

Right Angle (90°)
90° Examples: 90°

Right angles form perfect L-shapes. They are exactly one quarter of a full circle.

Obtuse Angle (90° to 180°)
135° Examples: 91°, 120°, 150°, 179°

Obtuse angles are larger than a right angle but smaller than a straight line.

Straight Angle (180°)
180° Examples: 180°

Straight angles form a perfectly flat line. They are exactly half of a full circle.

Angle Classification Rules and Properties
Angle Types: Acute, Right, Obtuse, Straight
Angle Classification
Key definitions:

Acute angle: Measures between 0° and 90°

Right angle: Measures exactly 90°

Obtuse angle: Measures between 90° and 180°

Straight angle: Measures exactly 180°

Complete methodology:
  1. Identify the vertex: Locate the point where the two rays meet
  2. Measure the angle: Use a protractor or given measurement
  3. Compare to benchmarks: Compare to 90° and 180°
  4. Classify the angle: Determine which category it fits
Tip 1: Remember "acute" means sharp/small, so acute angles are small (less than 90°).
Tip 2: Right angles form perfect L-shapes and are often marked with a small square.
Tip 3: Obtuse angles are wider than right angles but not completely flat.
Tip 4: Straight angles form a straight line and measure exactly 180°.
Common errors: Confusing acute and obtuse angles, misreading protractor measurements, forgetting that right angles are exactly 90°.
Exam preparation: Practice identifying angles visually, memorize the degree ranges, know the characteristics of each type.
Classification rules to know:

• Acute angle: 0° < angle < 90°

• Right angle: angle = 90°

• Obtuse angle: 90° < angle < 180°

• Straight angle: angle = 180°

Questions & Answers

Question: I sometimes get confused between acute and obtuse angles. Can you explain the difference more clearly?

Answer: Great question! The key difference is size:

  • Acute angles are SMALLER than a right angle (less than 90°). Think of them as "sharp" or "cute" - like the tip of a pencil.
  • Obtuse angles are LARGER than a right angle but smaller than a straight line (between 90° and 180°). Think of them as "wide" or "blunt" - like a wide-open door.

Memory trick: "Acute" sounds like "cute" - small and sharp. "Obtuse" means dull - wide and blunt.

Examples: 30° is acute, 120° is obtuse. Both are different from a right angle (90°).

Question: How can I help my child practice identifying angles at home? Are there everyday examples?

Answer: Absolutely! Here are some practical ways to practice at home:

  • Acute angles: Clock hands at 2:00, the tip of scissors, the letter "V", open pizza slice
  • Right angles: Corners of books, walls meeting floors, windows, table corners
  • Obtuse angles: Clock hands at 10:10, opened book laying flat, fully opened fan
  • Straight angles: Flat desk edge, horizon line, fully stretched arm

You can also use a paper plate cut in half to demonstrate a straight angle, or fold paper to create right angles. Real-world connections make learning stick!

Question: What happens if an angle measures exactly 90°? Is it still acute or obtuse?

Answer: An angle that measures exactly 90° is called a right angle, not acute or obtuse!

Here's the complete classification system:

  • Acute: Less than 90° (0° < angle < 90°)
  • Right: Exactly 90° (angle = 90°)
  • Obtuse: More than 90° but less than 180° (90° < angle < 180°)
  • Straight: Exactly 180° (angle = 180°)

Right angles are special because they form perfect L-shapes and are commonly found in rectangles and squares. They're the boundary between acute and obtuse angles.