Solved Exercises on Angles and Degree Measure in Grade 4

Master angles and degree measure: identifying types of angles, measuring with protractors, and understanding angle relationships through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Identifying angle types
Exercise 1
Name the following angles and classify them as acute, right, or obtuse:
∠ABC = 45°, ∠DEF = 90°, ∠GHI = 120°
Definition:

Angle types: Acute (less than 90°), Right (exactly 90°), Obtuse (more than 90° but less than 180°)

Classification method:
  1. Compare the angle measure to 90°
  2. If measure < 90° → Acute angle
  3. If measure = 90° → Right angle
  4. If measure > 90° → Obtuse angle
∠ABC = 45°
Acute
∠DEF = 90°
Right
∠GHI = 120°
Obtuse
Step 1: Compare ∠ABC to 90°

45° < 90°, so ∠ABC is acute

Step 2: Compare ∠DEF to 90°

90° = 90°, so ∠DEF is right

Step 3: Compare ∠GHI to 90°

120° > 90°, so ∠GHI is obtuse

∠ABC = 45° (acute), ∠DEF = 90° (right), ∠GHI = 120° (obtuse)
Final answer:

∠ABC = 45° (acute angle), ∠DEF = 90° (right angle), ∠GHI = 120° (obtuse angle)

Applied rules:

• Classification: Compare angle measure to 90°

• Acute: Less than 90°

• Right: Exactly 90°

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

2 Measuring angles with protractor
Exercise 2
Using a protractor, measure the angle shown in the diagram below and identify its type.
[Imagine a diagram showing an angle with vertex O and rays OA and OB forming an angle of approximately 70°]
Definition:

Protractor: Tool used to measure angles in degrees

Angle measurement
70°
Angle type
Acute
Step 1: Place protractor correctly

Place the center of the protractor on the vertex of the angle

Step 2: Align one ray

Align one ray of the angle with the 0° mark on the protractor

Step 3: Read the measurement

Read where the other ray crosses the protractor scale

Step 4: Classify the angle

Since 70° < 90°, the angle is acute

Measured angle = 70° (acute angle)
Final answer:

The measured angle is 70°, which is an acute angle because it is less than 90°.

Applied rules:

• Protractor placement: Center on vertex, align with 0° mark

• Reading: Follow the scale to the second ray

• Classification: Compare to 90° for identification

3 Finding missing angle measures
Exercise 3
Two angles form a straight line. One angle measures 110°. What is the measure of the other angle?
Definition:

Supplementary angles: Two angles that add up to 180°

Known angle
110°
Straight line
180°
Missing angle
70°
Step 1: Understand the relationship

Two angles forming a straight line are supplementary, so they add up to 180°

Step 2: Set up equation

Known angle + Unknown angle = 180°

110° + Unknown angle = 180°

Step 3: Solve for unknown angle

Unknown angle = 180° - 110° = 70°

Step 4: Verify the answer

110° + 70° = 180° ✓

The missing angle measures 70°
Final answer:

The measure of the other angle is 70°.

Applied rules:

• Supplementary angles: Sum to 180°

• Equation solving: Subtract known angle from total

• Verification: Check that angles sum to 180°

Rules and methods, laws,...
Acute: < 90°
Angle Types
Acute Angle
0° < θ < 90°
Less than 90 degrees
Right Angle
θ = 90°
Exactly 90 degrees
Obtuse Angle
90° < θ < 180°
Greater than 90 degrees

Visual Angle Guide

📐
Acute Angle (0°-90°)
Smaller than a right angle. Think of the sharp corner of a slice of pizza.
Example: 30°, 45°, 60°
Right Angle (90°)
Forms a perfect L shape. Found in squares and rectangles.
Example: Corner of a book
Obtuse Angle (90°-180°)
Larger than a right angle but smaller than a straight line.
Example: 120°, 135°, 150°
Using a Protractor
1
Center on Vertex
2
Align Ray with 0°
3
Read Second Ray
Key Concepts & Practice Tips
Supplementary: A + B = 180°
Angle Relationships
Key definitions:

Vertex: The point where two rays meet to form an angle

Rays: Lines extending from the vertex that form the sides of the angle

Degree: Unit of measurement for angles

Complete methodology:
  1. Identify the vertex: Locate the point where the angle is formed
  2. Recognize the angle type: Compare to 90° reference
  3. Measure if needed: Use a protractor for precision
  4. Apply angle relationships: Use supplementary or complementary rules
Tip 1: Remember: Acute angles are "cute" because they're small!
Tip 2: A right angle makes a perfect L-shape, like the corner of a piece of paper.
Tip 3: When two angles form a straight line, they always add up to 180°.
Tip 4: Always double-check your protractor reading by ensuring it's properly aligned.
Common errors: Misreading protractor scale, confusing angle types, misaligning protractor.
Exam preparation: Practice identifying angle types, master protractor use, memorize angle relationships.
Facts to remember:

• Acute angle: Less than 90°

• Right angle: Exactly 90°

• Obtuse angle: Greater than 90° but less than 180°

• Straight angle: Exactly 180°

• Supplementary angles: Sum to 180°

Questions & Answers

Question: I sometimes get confused between acute and obtuse angles. How can I remember which is which?

Answer: Great question! Here are some memory tricks:

  • Acute angles are "cute" and small - they are less than 90°, just like cute little things are small.
  • Obtuse angles are "obviously" big - they are greater than 90°, so they're obviously larger than right angles.

Another way to remember: Acute starts with "A" like "All small", while Obtuse starts with "O" like "Obviously large".

You can also visualize: an acute angle is like the sharp corner of a slice of pizza, while an obtuse angle is like the wide opening of an open door.

Question: When using a protractor, how do I know which number to read? There are two scales on my protractor!

Answer: This is a very common confusion! Here's how to choose the correct scale:

  • First, align the protractor's center with the angle's vertex and one ray with the 0° mark.
  • Look at the other ray of the angle.
  • If the angle appears to be less than 90° (acute), choose the smaller number.
  • If the angle appears to be greater than 90° (obtuse), choose the larger number.

Alternatively, follow the inner or outer scale consistently depending on which direction you placed the 0° mark. If you aligned with the inner 0°, use the inner scale; if with the outer 0°, use the outer scale.

Always estimate first whether your angle looks acute or obtuse to verify your measurement makes sense!

Question: Why do two angles that form a straight line always add up to 180°?

Answer: This happens because of how we define degrees and straight lines:

  • A full circle has 360°, representing a complete rotation.
  • A straight line represents half a rotation, so it has 360° ÷ 2 = 180°.
  • When two angles form a straight line, together they make that half rotation.

Think of it like cutting a semicircle in half - no matter how you cut it, the two pieces will always add up to the full semicircle (180°).

These pairs of angles are called "supplementary angles" - they supplement each other to make a straight line!