Solved Exercises on Angle Word Problems in 4th Grade Math

Master measuring angles through practical word problems: acute, right, obtuse, straight angles, and real-world applications with detailed solutions.

Solution: Exercises 1 to 3
1 Acute Angle Problem
Exercise 1
Sarah is drawing a triangle. One angle measures 45°. What type of angle is this? How do you know?
Definition:

Acute angle: An angle that measures less than 90°

Right angle: An angle that measures exactly 90°

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

Straight angle: An angle that measures exactly 180°

Classification method:
  1. Compare the given angle measure to 90°
  2. If less than 90°, it's acute
  3. If equal to 90°, it's right
  4. If greater than 90° but less than 180°, it's obtuse
Given angle
45°
Classification
Acute angle
Step 1: Compare to 90°

45° < 90°, so the angle is less than a right angle

Step 2: Apply classification rule

Any angle less than 90° is classified as acute

Step 3: State the answer

The 45° angle is an acute angle

45° is an acute angle because 45° < 90°
Final answer:

The 45° angle is an acute angle because it measures less than 90°.

Applied rules:

• Angle classification: Compare to 90° reference

• Acute definition: Less than 90°

• Measurement: Use degree units (°)

2 Complementary Angles
Exercise 2
Two angles are complementary. One angle measures 35°. What is the measure of the other angle?
Definition:

Complementary angles: Two angles whose sum equals 90°

Supplementary angles: Two angles whose sum equals 180°

Given angle
35°
Complementary sum
90°
Unknown angle
55°
Step 1: Recall complementary definition

Complementary angles sum to 90°

Step 2: Set up equation

Known angle + Unknown angle = 90°

35° + Unknown angle = 90°

Step 3: Solve for unknown angle

Unknown angle = 90° - 35° = 55°

The other angle measures 55°
Final answer:

The other angle measures 55° because 35° + 55° = 90°.

Applied rules:

• Complementary angles: Sum equals 90°

• Subtraction: To find missing angle, subtract known from total

• Verification: Check that angles sum correctly

3 Obtuse Angle Problem
Exercise 3
During a hiking trip, Tom noticed the angle formed by the sun's rays hitting the mountain slope was 125°. What type of angle is this? Explain your reasoning.
Definition:

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

Given angle
125°
Classification
Obtuse angle
Range check
90° < 125° < 180°
Step 1: Compare to 90°

125° > 90°, so it's greater than a right angle

Step 2: Compare to 180°

125° < 180°, so it's less than a straight angle

Step 3: Apply classification rule

Since 90° < 125° < 180°, it's an obtuse angle

Step 4: Verify the answer

Obtuse angles are between 90° and 180°, which matches 125°

125° is an obtuse angle because 90° < 125° < 180°
Final answer:

The 125° angle is an obtuse angle because it measures greater than 90° but less than 180°.

Applied rules:

• Obtuse definition: Between 90° and 180°

• Comparison: Check against both boundaries

• Verification: Confirm angle fits range

Angle Classification Rules and Methods
Acute: 0° < θ < 90°
Acute Angle
Right Angle
θ = 90°
Exact 90 degrees
Obtuse Angle
90° < θ < 180°
Between 90° and 180°
Straight Angle
θ = 180°
Exactly 180 degrees
Key definitions:

Complementary angles: Two angles that sum to 90°

Supplementary angles: Two angles that sum to 180°

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

Complete methodology:
  1. Read the problem carefully: Identify given angle measures
  2. Classify angles: Determine if acute, right, obtuse, or straight
  3. Apply relationships: Use complementary (90°) or supplementary (180°) rules
  4. Calculate missing angles: Use subtraction when needed
  5. Verify the result: Check calculations and classifications
Tip 1: Remember the acronym "ACUTE" - Angles CUnder TEn degrees.
Tip 2: Think of the corner of a piece of paper as a right angle (90°).
Tip 3: For complementary angles, subtract the known angle from 90°.
Tip 4: Always check that your answer makes sense in the context of the problem.
Common errors: Confusing acute with obtuse, forgetting angle sums, misreading protractors.
Exam preparation: Practice angle classification, memorize complementary and supplementary relationships, work with protractor measurements.
Formulas to know by heart:

• Complementary angles: A + B = 90°

• Supplementary angles: A + B = 180°

• Acute angle: 0° < θ < 90°

• Right angle: θ = 90°

• Obtuse angle: 90° < θ < 180°

• Straight angle: θ = 180°

Solution: Exercises 4 to 5
4 Supplementary Angles
Exercise 4
Two angles are supplementary. One angle measures 110°. What is the measure of the other angle?
Definition:

Supplementary angles: Two angles whose sum equals 180°

Given angle
110°
Supplementary sum
180°
Unknown angle
70°
Step 1: Recall supplementary definition

Supplementary angles sum 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 result

110° + 70° = 180° ✓

The other angle measures 70°
Final answer:

The other angle measures 70° because 110° + 70° = 180°.

Applied rules:

• Supplementary angles: Sum equals 180°

• Subtraction: To find missing angle, subtract known from total

• Verification: Check that angles sum to 180°

5 Real-World Application
Exercise 5
At 3 o'clock, the hour hand and minute hand of a clock form an angle. What type of angle do they form? Calculate its measure.
Definition:

Clock angles: Each hour mark represents 30° (360° ÷ 12 hours)

Clock setup
3 o'clock
Angle calculation
3 × 30° = 90°
Classification
Right angle
Step 1: Understand clock structure

A full circle is 360°, divided into 12 hours

Each hour represents 360° ÷ 12 = 30°

Step 2: Calculate the angle at 3 o'clock

At 3 o'clock, the hour hand points to 3

The minute hand points to 12

They are separated by 3 hour marks: 3 × 30° = 90°

Step 3: Classify the angle

Since the angle measures exactly 90°, it's a right angle

Step 4: Verify the result

At 3 o'clock, the hands form a perfect L-shape, confirming it's 90°

At 3 o'clock, the hands form a 90° right angle
Final answer:

At 3 o'clock, the hands form a 90° right angle because 3 × 30° = 90°.

Applied rules:

• Clock angles: Each hour = 30° (360° ÷ 12)

• Right angle: Exactly 90°

• Real-world application: Connect mathematical concepts to everyday objects

Angle Properties and Relationships Guide
Complementary: A + B = 90°
Angle Relationships
Key definitions:

Acute angle: Measures between 0° and 90°

Right angle: Measures exactly 90°

Obtuse angle: Measures between 90° and 180°

Complementary angles: Two angles that sum to 90°

Supplementary angles: Two angles that sum to 180°

Complete methodology:
  1. Analyze the problem: Identify what's given and what's asked
  2. Classify angles: Determine angle types based on measures
  3. Apply relationships: Use complementary or supplementary rules
  4. Calculate missing values: Use arithmetic operations
  5. Verify the solution: Check calculations and reasonableness
Tip 1: To remember complementary angles, think "C" for "Corner" (right angle).
Tip 2: For supplementary angles, think "S" for "Straight" line (180°).
Tip 3: Draw diagrams to visualize angle relationships.
Tip 4: Always include the degree symbol (°) in your answers.
Common errors: Mixing up complementary and supplementary, forgetting angle ranges, miscounting hour marks on clocks.
Memory aid: "Acute" sounds like "cute" - small and adorable (small angles). "Obtuse" sounds like "obvious" - big and obvious (large angles).
Formulas to know by heart:

• Complementary: A + B = 90°

• Supplementary: A + B = 180°

• Clock angles: Each hour = 30°

• Acute: 0° < θ < 90°

• Right: θ = 90°

• Obtuse: 90° < θ < 180°

• Straight: θ = 180°

Visual Angle Relationships
Understanding Angle Types
Visual representation of different angle types and their relationships:

Key Concepts:

  • Acute angles are less than 90° (sharp angles)
  • Right angles are exactly 90° (perfect L-shape)
  • Obtuse angles are between 90° and 180° (wide angles)
  • Complementary angles sum to 90°
  • Supplementary angles sum to 180°

Questions & Answers

Question: I'm confused about how to tell if an angle is acute or obtuse just by looking at it. Can you explain the difference?

Answer: Great question! Here's how to visually distinguish between acute and obtuse angles:

  • Acute angles: Look narrower and sharper than a right angle. They're "cute" and small, less than 90°. Think of the tip of a slice of pizza.
  • Obtuse angles: Look wider and more open than a right angle. They're bigger than 90° but smaller than 180°. Think of an open book lying flat.

A helpful memory trick: "Acute" sounds like "cute" - small and adorable (small angles). "Obtuse" sounds like "obvious" - big and obvious (large angles).

To check yourself, compare to the corner of a piece of paper (90°). If it's smaller, it's acute. If it's larger, it's obtuse!

Question: How do I know when to use complementary vs. supplementary angles in word problems?

Answer: Here's how to identify which relationship to use:

  • Complementary angles (sum to 90°): Look for words like "corner," "L-shape," "perpendicular," "right angle," or when two angles form a right angle together.
  • Supplementary angles (sum to 180°): Look for words like "straight line," "linear pair," "flat surface," "straight angle," or when two angles form a straight line.

Memory aids:

  • "C" for Complementary = "Corner" (90° angle)
  • "S" for Supplementary = "Straight" (180° line)

Always read the problem carefully to see if it mentions forming a right angle (complementary) or a straight line (supplementary).

Question: When solving clock problems, how do I calculate the angle between the hands?

Answer: Here's the systematic approach for clock angle problems:

  • Basic principle: A full circle is 360°, divided into 12 hours, so each hour mark = 360° ÷ 12 = 30°
  • Hour hand: Points to the exact hour at o'clock times
  • Minute hand: Points to 12 at o'clock times
  • Angle calculation: Count the number of hour spaces between the hands and multiply by 30°

Examples:

  • At 3 o'clock: Hands are 3 spaces apart → 3 × 30° = 90°
  • At 6 o'clock: Hands are 6 spaces apart → 6 × 30° = 180°
  • At 9 o'clock: Hands are 3 spaces apart → 3 × 30° = 90°

For times that aren't on the hour, you'd also need to account for the movement of the hour hand, but for basic problems, focus on the hour positions.