Grade: 4 Subject: Math Unit: Angles and Geometry Lesson: 4 of 6 SAT: Geometry+Trigonometry ACT: Math

Word Problems

Learn

In this lesson, you will solve real-world problems involving angles. These word problems will help you see how angle measurement and classification apply to everyday situations.

Problem-Solving Strategy:

  1. Read the problem carefully
  2. Identify what you know and what you need to find
  3. Draw a diagram if it helps
  4. Solve using your angle knowledge
  5. Check that your answer makes sense

Examples

Study these worked examples before attempting the practice problems.

Example 1: Clock Hands

Problem: What type of angle do the clock hands form at 3:00?

Solution: At 3:00, the minute hand points to 12 and the hour hand points to 3. This creates a 90-degree angle, which is a right angle.

Example 2: Ladder Against a Wall

Problem: A ladder leans against a wall making a 65-degree angle with the ground. What type of angle is this?

Solution: Since 65 degrees is less than 90 degrees, this is an acute angle.

Practice Quiz

Solve these 10 word problems. Click on each question to reveal the answer.

Question 1: A pizza is cut into 4 equal slices. What is the angle at the tip of each slice?

Answer: 90 degrees. A full circle is 360 degrees, so 360 / 4 = 90 degrees per slice.

Question 2: Sarah opens a book so that the two covers form a 60-degree angle. Is this angle acute, right, or obtuse?

Answer: Acute. 60 degrees is less than 90 degrees.

Question 3: A ramp makes a 15-degree angle with the ground. A second ramp makes a 25-degree angle. Which ramp is steeper?

Answer: The second ramp (25 degrees) is steeper because it has a larger angle with the ground.

Question 4: At 6:00, what type of angle do the clock hands form?

Answer: A straight angle (180 degrees). The hands point in opposite directions.

Question 5: A door is open at a 110-degree angle from the wall. What type of angle is this?

Answer: Obtuse. 110 degrees is greater than 90 degrees but less than 180 degrees.

Question 6: Two roads meet at an intersection. One angle at the intersection measures 75 degrees. What does the angle directly across from it measure?

Answer: 75 degrees. Angles directly across from each other (vertical angles) are equal.

Question 7: A slice of pie has an angle of 45 degrees at its tip. How many slices of this size would make a whole pie?

Answer: 8 slices. Since 360 / 45 = 8.

Question 8: A kite string makes a 50-degree angle with the ground. If the angle increases to 70 degrees, is the kite flying higher or lower in the sky?

Answer: Higher. A larger angle with the ground means the string is pointing more upward.

Question 9: Two angles in a triangle measure 60 degrees and 80 degrees. What is the measure of the third angle?

Answer: 40 degrees. The angles in a triangle add up to 180 degrees. 180 - 60 - 80 = 40 degrees.

Question 10: A skateboard ramp needs to have an angle less than 45 degrees to be safe for beginners. Marcus builds a ramp with a 38-degree angle. Is it safe for beginners?

Answer: Yes, it is safe. 38 degrees is less than 45 degrees.

Check Your Understanding

Review your answers above. Make sure you understand how to apply angle concepts to real-world situations. If you struggled with any problems, review the Examples section.

Next Steps

  • Look for angles in your everyday life - clocks, doors, buildings
  • Practice estimating angles before measuring them
  • Move on to Common Mistakes to learn what errors to avoid