Solved Exercises on Measuring Angles with Protractor in Grade 4

Master measuring angles with a protractor: acute, right, obtuse, and straight angles through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Measuring Acute Angle
Exercise 1
Measure the acute angle shown in the diagram using a protractor. The angle appears to be less than 90°.
Definition:

Acute angle: An angle that measures less than 90°

Measurement method:
  1. Place the center of the protractor at the vertex of the angle
  2. Align one side of the angle with the baseline of the protractor
  3. Read the measurement where the other side intersects the protractor scale
  4. For acute angles, use the smaller number on the scale
45°
Step 1: Position the protractor

Place the center hole of the protractor directly over the vertex of the angle

Step 2: Align the baseline

Make sure one ray of the angle lines up with the straight edge of the protractor

Step 3: Read the measurement

Follow the other ray to see where it crosses the curved edge of the protractor

Step 4: Identify the correct scale

Since it's an acute angle (less than 90°), choose the smaller number on the scale

The acute angle measures 45°
Final answer:

The angle measures 45°, which is an acute angle

Applied rules:

• Protractor positioning: Center must be on the vertex

• Baseline alignment: One side must align with protractor base

• Scale selection: Use inner scale for angles opening right, outer for angles opening left

2 Measuring Right Angle
Exercise 2
Measure the right angle formed by two perpendicular lines using a protractor.
Definition:

Right angle: An angle that measures exactly 90°

90°
Step 1: Position the protractor

Place the center of the protractor at the corner where the two lines meet

Step 2: Align with one line

Line up one of the perpendicular lines with the baseline of the protractor

Step 3: Check the other line

The other line should align with the 90° mark on the protractor

Step 4: Verify the measurement

Confirm that the angle measures exactly 90°

The right angle measures 90°
Final answer:

The angle measures 90°, which is a right angle

Applied rules:

• Perpendicular lines: Always form 90° angles

• Right angle identification: Exactly 90°

• Measurement verification: Should match 90° mark on protractor

3 Measuring Obtuse Angle
Exercise 3
Measure the obtuse angle shown in the diagram using a protractor. The angle appears to be greater than 90° but less than 180°.
Definition:

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

120°
Step 1: Position the protractor

Place the center of the protractor at the vertex of the angle

Step 2: Align the baseline

Align one side of the angle with the baseline of the protractor

Step 3: Read the measurement

Find where the other side intersects the protractor scale

Step 4: Select the larger scale

Since it's an obtuse angle (greater than 90°), use the larger number on the scale

The obtuse angle measures 120°
Final answer:

The angle measures 120°, which is an obtuse angle

Applied rules:

• Obtuse angle range: Greater than 90° and less than 180°

• Scale selection: For obtuse angles, choose the larger number

• Angle classification: Compare measurement to 90° and 180°

Rules and methods, laws,...
Acute < 90°
Acute Angle
Right Angle
= 90°
Exactly 90 degrees
Obtuse Angle
90° < θ < 180°
Between 90° and 180°
Straight Angle
= 180°
Exactly 180 degrees
Key definitions:

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

Rays: The two lines that form the sides of an angle

Protractor: A tool used to measure angles in degrees

Complete methodology:
  1. Position the protractor: Place center on the vertex of the angle
  2. Align the baseline: Make one side of the angle align with the protractor's base
  3. Read the scale: Follow the other side to see where it intersects the protractor
  4. Select the correct measurement: Choose based on angle type (acute, obtuse, etc.)
Tip 1: Always place the center of the protractor exactly on the vertex.
Tip 2: Look for the small marks on the protractor - each represents 1 degree.
Tip 3: For angles opening to the left, use the outer scale; for angles opening to the right, use the inner scale.
Tip 4: Estimate the angle type before measuring to verify your reading.
Common errors: Misaligning the protractor, reading the wrong scale, not placing center on vertex.
Exam preparation: Practice with various angle orientations, memorize angle classifications, verify measurements.
Formulas to know by heart:

• Acute angle: 0° < angle < 90°

• Right angle: angle = 90°

• Obtuse angle: 90° < angle < 180°

• Straight angle: angle = 180°

• Full rotation: angle = 360°

Solution: Exercises 4 to 5
4 Measuring Straight Angle
Exercise 4
Measure the straight angle formed by two rays pointing in opposite directions using a protractor.
Definition:

Straight angle: An angle that measures exactly 180°

180°
Step 1: Position the protractor

Place the center of the protractor at the vertex where the two rays meet

Step 2: Align with one ray

Line up one of the rays with the baseline of the protractor

Step 3: Check the other ray

The other ray should align with the 180° mark on the protractor

Step 4: Verify the measurement

Confirm that the angle measures exactly 180°

The straight angle measures 180°
Final answer:

The angle measures 180°, which is a straight angle

Applied rules:

• Straight angle identification: Exactly 180°

• Opposite rays: Always form a straight angle

• Measurement verification: Should match 180° mark on protractor

5 Multiple Angle Measurement
Exercise 5
Measure multiple angles in a triangle using a protractor and verify that their sum equals 180°.
Definition:

Triangle angle sum: The sum of interior angles in any triangle is 180°

60°
70°
50°
Step 1: Measure first angle

Place protractor at the first vertex and measure the angle (e.g., 60°)

Step 2: Measure second angle

Move protractor to the second vertex and measure the angle (e.g., 70°)

Step 3: Measure third angle

Move protractor to the third vertex and measure the angle (e.g., 50°)

Step 4: Verify the sum

Add all three angles: 60° + 70° + 50° = 180° ✓

Sum of angles: 60° + 70° + 50° = 180°
Final answer:

The three angles measure 60°, 70°, and 50° respectively. Their sum is 180°, confirming the triangle angle sum property.

Applied rules:

• Triangle angle sum: Interior angles of a triangle always sum to 180°

• Multiple measurements: Each angle must be measured separately

• Verification: Sum should equal 180°

Key Concepts: Angles and Protractor Measurement
Σ Interior Angles = 180°
Triangle Angle Sum
Key definitions:

Angle: The space between two intersecting lines measured in degrees

Degree: A unit of measurement for angles (symbol: °)

Protractor: A semicircular tool marked with degrees from 0° to 180°

Complete methodology:
  1. Identify the angle: Locate the vertex and two rays forming the angle
  2. Position the protractor: Center hole over the vertex
  3. Align the baseline: One ray aligned with protractor base
  4. Read the scale: Follow the other ray to its intersection point
  5. Verify the measurement: Check against angle type classification
Tip 1: Always read the protractor from the side where the angle opens.
Tip 2: The center of the protractor has a small hole - this goes exactly on the vertex.
Tip 3: For accuracy, make sure the protractor is flat against the paper.
Tip 4: If the rays are too short, extend them with a ruler to reach the protractor scale.
Common errors: Misaligning the protractor, reading the wrong scale, not placing center on vertex, misreading degrees.
Exam preparation: Practice with various angle orientations, memorize angle classifications, verify measurements by estimation.
Formulas to know by heart:

• Acute angle: 0° < angle < 90°

• Right angle: angle = 90°

• Obtuse angle: 90° < angle < 180°

• Straight angle: angle = 180°

• Triangle angle sum: ∠A + ∠B + ∠C = 180°

Questions & Answers

Question: I have trouble knowing which scale to read on the protractor. Sometimes I get confused between the inner and outer numbers. Can you explain how to choose the right one?

Answer: Great question! The choice of scale depends on the direction the angle opens:

  • If the angle opens to the right (counterclockwise from 0°), use the inner scale that starts at 0° on the right
  • If the angle opens to the left (clockwise from 0°), use the outer scale that starts at 0° on the left

A helpful trick is to estimate the angle first:

  • If it looks like an acute angle (less than 90°), choose the smaller number
  • If it looks like an obtuse angle (more than 90°), choose the larger number

Always verify your measurement makes sense with your visual estimate!

Question: When I measure an angle, sometimes my answer is slightly off from the expected answer. How accurate should I be when measuring with a protractor?

Answer: For Grade 4 students, being within 1-2 degrees is considered very good accuracy. Here are tips for precision:

  • Make sure the protractor is perfectly centered on the vertex
  • Ensure one ray aligns exactly with the baseline
  • Look straight down at the protractor to avoid parallax error
  • Estimate the exact position if the ray falls between two degree marks

Small variations are normal due to the physical limitations of the tool and human measurement. Focus on getting the closest whole number and understanding the angle classification.

Question: What should I do if the rays of the angle are too short to reach the edge of the protractor?

Answer: This is a common situation! Here's how to handle it:

  • Use a ruler to carefully extend the rays beyond the angle
  • Make sure to extend the lines straight in the same direction
  • Once extended, read the measurement where the extended line meets the protractor scale

Be careful to maintain the original direction of the ray when extending it. The angle measurement will remain the same regardless of the length of the rays.

Remember: the size of an angle doesn't depend on the length of its sides, only on how much the sides diverge from each other.