Lines and Angles

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Answer Key & Explanations

Lines and Angles · Grade 4 · Worksheet 3

1. Kaia is helping her grandmother design a quilt. She draws a pattern on paper that has two straight lines that cross each other. One of the angles formed where the lines cross is 125 degrees. What type of angle is this? Answer: obtuse angle Solution: Recall the definitions of angle types. A right angle is exactly 90 degrees. An acute angle is less than 90 degrees.
   Full step-by-step solution

   Step 1: Recall the definitions of angle types. Step 2: A right angle is exactly 90 degrees. Step 3: An acute angle is less than 90 degrees. Step 4: An obtuse angle is greater than 90 degrees but less than 180 degrees. Step 5: 125 degrees is greater than 90 and less than 180. Step 6: Therefore, the angle is an obtuse angle. The answer is obtuse angle.

2. Noah is drawing a large clock on the board. The clock is a circle with two lines starting from the center. One line points directly to the number 12, and the other line points to the number 4. What type of angle is formed between these two lines? Answer: obtuse angle Solution: Visualize the clock face. The numbers are evenly spaced around the circle. There are 12 numbers around the full 360-degree circle.
   Full step-by-step solution

   Step 1: Visualize the clock face. The numbers are evenly spaced around the circle. Step 2: There are 12 numbers around the full 360-degree circle. Each hour represents 360/12 = 30 degrees. Step 3: From 12 to 4, there are 4 hours: 12 to 1, 1 to 2, 2 to 3, 3 to 4. That is 4 x 30 = 120 degrees. Step 4: Compare 120 degrees to a right angle (90 degrees). Since 120 > 90, the angle is larger than a right angle. Step 5: An angle larger than 90 degrees but less than 180 degrees is called an obtuse angle. Therefore, the angle between the 12 and the 4 on the clock is an obtuse angle.

3. Mason is drawing a diagram of a city intersection. He draws a horizontal line to represent Main Street. From a point on Main Street, he draws a ray pointing upward and to the right, forming an opening that is smaller than a square corner. What type of angle is formed between Main Street and the ray? Answer: acute angle Solution: Identify the two lines that form the angle: Main Street (horizontal line) and the ray (pointing upward and to the right). Picture the angle they create. The ray is not straight up (which would make a right angle) but is tilted so the opening is smaller than 90 degrees.
   Full step-by-step solution

   Step 1: Identify the two lines that form the angle: Main Street (horizontal line) and the ray (pointing upward and to the right). Step 2: Picture the angle they create. The ray is not straight up (which would make a right angle) but is tilted so the opening is smaller than 90 degrees. Step 3: An angle smaller than a right angle is called an acute angle. The answer is acute angle.

4. Mere is drawing a geometric figure on a piece of paper. She starts at a point labeled A and draws a straight line that goes on forever in one direction only, passing through point B. Then she draws a straight line that starts at point C and goes on forever in both directions, passing through point D. What are the names of the two geometric figures Mere drew? Answer: ray AB and line CD Solution: Identify the first figure. It starts at point A and goes through point B, continuing forever in one direction only. This matches the definition of a ray.
   Full step-by-step solution

   Step 1: Identify the first figure. It starts at point A and goes through point B, continuing forever in one direction only. This matches the definition of a ray. We name it ray AB (starting at A and passing through B). Step 2: Identify the second figure. It starts at point C and goes through point D, continuing forever in both directions. This matches the definition of a line. We name it line CD. Step 3: The two geometric figures are ray AB and line CD.

5. Sophia is drawing a clock face for her art project. She draws two hands on the clock. One hand points to 12 and the other points to 3. What type of angle is formed between the two clock hands? Answer: right angle Solution: Look at the positions of the clock hands. One is at 12 (straight up) and the other is at 3 (pointing right). Step 2: The two hands meet at the center of the clock.
   Full step-by-step solution

   Step 1: Look at the positions of the clock hands. One is at 12 (straight up) and the other is at 3 (pointing right). Step 2: The two hands meet at the center of the clock. Step 3: The angle between 12 and 3 on a clock is exactly one quarter of a full circle. Step 4: A quarter-circle angle is called a right angle. The answer is right angle.

6. Aroha is drawing a map of her neighborhood. She draws a straight path from her house to the library. Then, she draws another path from the library to the park. The two paths meet at the library, forming an angle. If the angle between the two paths is smaller than a right angle, what type of angle is it? Answer: acute angle Solution: Recall the types of angles: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are more than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.
   Full step-by-step solution

   Step 1: Recall the types of angles: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are more than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees. Step 2: The problem says the angle is smaller than a right angle. A right angle is 90 degrees. Step 3: An angle smaller than a right angle is called an acute angle. The answer is acute angle.

7. Sophia is drawing a map of her neighborhood. She draws a line that starts at her house and goes straight to the park, but it only goes in one direction and has an endpoint at her house. What geometric figure did Sophia draw from her house to the park? Answer: C. Ray Solution: A line segment has two endpoints and does not extend forever. A ray has one endpoint and extends forever in one direction. A line has no endpoints and extends forever in both directions.
   Full step-by-step solution

   Step 1: A line segment has two endpoints and does not extend forever. Step 2: A ray has one endpoint and extends forever in one direction. Step 3: A line has no endpoints and extends forever in both directions. Step 4: A point is just a location, with no length or direction. Sophia's figure starts at her house (one endpoint) and goes straight to the park, but it doesn't continue past the park. Since it has one endpoint and goes in one direction, it is a ray. The correct answer is Ray.