Worksheet Answers: Measuring Angles with Protractor in Grade 4

Complete worksheet answers for measuring angles with a protractor: detailed solutions for acute, right, obtuse, and straight angles with step-by-step explanations.

Worksheet Answers: Exercises 1 to 3
1 Acute Angle Measurement
Exercise 1
Measure the acute angle shown in the diagram using a protractor. The angle appears to be approximately 35°.
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
35°
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

Answer: 35°

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

Verification:

The angle measures 35°, which is less than 90°, confirming it's 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 Right Angle Measurement
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°

Answer: 90°

This is a right angle because it measures exactly 90°

Verification:

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 Obtuse Angle Measurement
Exercise 3
Measure the obtuse angle shown in the diagram using a protractor. The angle appears to be approximately 145°.
Definition:

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

145°
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

Answer: 145°

This is an obtuse angle because it measures greater than 90° and less than 180°

Verification:

The angle measures 145°, which is greater than 90° and less than 180°, confirming it's 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°

Detailed Summary: Measuring Angles with Protractor
Key Concepts:

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°

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

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

Acute Angle
0° < θ < 90°
Less than 90 degrees
Right Angle
= 90°
Exactly 90 degrees
Obtuse Angle
90° < θ < 180°
Between 90° and 180°
Straight Angle
= 180°
Exactly 180 degrees
Complete Measurement Method:
  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. 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.
Tip 5: If 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.
Accuracy standards: Being within 1-2 degrees is considered very good for Grade 4 students.
Important Rules:

• Acute angle: 0° < angle < 90°

• Right angle: angle = 90°

• Obtuse angle: 90° < angle < 180°

• Straight angle: angle = 180°

• Full rotation: angle = 360°

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

Σ Interior Angles = 180°
Triangle Angle Sum Property
Worksheet Answers: Exercises 4 to 5
4 Straight Angle Measurement
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°

Answer: 180°

This is a straight angle because it measures exactly 180°

Verification:

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 Triangle Angle Sum
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°

65°
55°
60°
Step 1: Measure first angle

Place protractor at the first vertex and measure the angle (e.g., 65°)

Step 2: Measure second angle

Move protractor to the second vertex and measure the angle (e.g., 55°)

Step 3: Measure third angle

Move protractor to the third vertex and measure the angle (e.g., 60°)

Step 4: Verify the sum

Add all three angles: 65° + 55° + 60° = 180° ✓

Answer: 65° + 55° + 60° = 180°

The sum of angles in a triangle is always 180°

Verification:

The three angles measure 65°, 55°, and 60° 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°

Questions & Answers

Question: How do I verify that my angle measurements are correct on the worksheet?

Answer: You can verify your angle measurements by:

  • Checking if the angle type matches the measurement (acute < 90°, right = 90°, obtuse > 90°)
  • Ensuring the protractor was properly positioned at the vertex
  • Verifying that one ray aligned with the baseline
  • Confirming you read the correct scale (inner vs outer)

For triangles, verify that all three angles sum to 180°.

Question: What should I do if I get a measurement that doesn't match the expected answer?

Answer: If your measurement doesn't match the expected answer:

  • Reposition the protractor to ensure the center is exactly on the vertex
  • Check that one ray is properly aligned with the baseline
  • Verify you're reading from the correct starting point (0°)
  • Consider if you're using the correct scale (inner vs outer)

Small differences (1-2 degrees) are normal due to measurement precision limits.

Question: How do I know which scale to use on the protractor?

Answer: Choose the scale based on the angle's orientation:

  • If the angle opens to the right (counterclockwise from baseline), use the inner scale
  • If the angle opens to the left (clockwise from baseline), use the outer scale
  • Start counting from 0° where your angle's first ray aligns with the baseline

The scale that starts at 0° where your first ray is aligned is the correct one to use.