Lines and Angles

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Answer Key & Explanations

Lines and Angles · Grade 4 · Worksheet 2

1. Matiu draws an angle that measures 120°. What type of angle is this? Answer: obtuse angle Solution: Recall the types of angles: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°). The given angle is 120°.
   Full step-by-step solution

   Step 1: Recall the types of angles: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°). Step 2: The given angle is 120°. Step 3: Since 120° is greater than 90° and less than 180°, it is an obtuse angle. The answer is an obtuse angle.

2. Isabella is drawing a large star for her art project. She notices that one of the points of the star forms a corner that is smaller than a right angle. What type of angle is that corner? Answer: acute angle Solution: Recall the types of angles: right angle (exactly 90°), acute angle (less than 90°), obtuse angle (more than 90°).
   Full step-by-step solution

   Step 1: Recall the types of angles: right angle (exactly 90°), acute angle (less than 90°), obtuse angle (more than 90°). Step 2: The problem says the corner is 'smaller than a right angle.' Step 3: Therefore, the angle is acute. Answer: acute angle.

3. Noah draws an angle that measures 91°. What type of angle is it? Answer: obtuse angle Solution: Recall the definitions: An acute angle measures less than 90°. A right angle measures exactly 90°. An obtuse angle measures more than 90° but less than 180°.
   Full step-by-step solution

   Step 1: Recall the definitions: An acute angle measures less than 90°. A right angle measures exactly 90°. An obtuse angle measures more than 90° but less than 180°. Step 2: Compare 91° to these definitions. Since 91° is greater than 90° and less than 180°, it is an obtuse angle. The answer is obtuse angle.

4. Emma is drawing a shape on a piece of paper. She starts at a point and draws a straight path that goes on forever in one direction, but stops at the starting point. What geometric figure did Emma draw: a line, a line segment, or a ray? Answer: ray Solution: A line goes on forever in both directions with no endpoints. A line segment has two endpoints and does not go on forever. A ray has one endpoint and goes on forever in one direction.
   Full step-by-step solution

   Step 1: A line goes on forever in both directions with no endpoints. Step 2: A line segment has two endpoints and does not go on forever. Step 3: A ray has one endpoint and goes on forever in one direction. Step 4: Emma's figure has one starting point and goes on forever in one direction, so it is a ray. The answer is ray.

5. Mason is building a wooden frame for a kite. He draws two lines that cross each other. One line goes straight up and down, and the other goes straight left to right. The angle where they meet looks like the corner of a square. What type of angle did Mason create? Answer: right angle Solution: Mason has two lines that cross: one vertical (up and down) and one horizontal (left to right). Step 2: The angle at the meeting point is the same as the corner of a square.
   Full step-by-step solution

   Step 1: Mason has two lines that cross: one vertical (up and down) and one horizontal (left to right). Step 2: The angle at the meeting point is the same as the corner of a square. Step 3: This type of angle is called a right angle because it measures 90 degrees. The answer is right angle.

6. Mason is building a wooden birdhouse. He draws a shape on his plywood that has one endpoint at point A and extends infinitely in one direction through point B. What geometric figure has Mason drawn? Answer: ray Solution: Identify the key details. The figure starts at point A (one endpoint). Step 2: The figure extends infinitely in one direction through point B.
   Full step-by-step solution

   Step 1: Identify the key details. The figure starts at point A (one endpoint). Step 2: The figure extends infinitely in one direction through point B. Step 3: A line extends infinitely in both directions. A line segment has two endpoints. A ray has one endpoint and extends infinitely in one direction. Step 4: Since it has exactly one endpoint and goes forever in one direction, the figure is a ray. The answer is a ray.

7. Mason is drawing a diagram of his bedroom for a school project. He draws a corner of his room where two walls meet. The angle inside the corner where the two walls meet looks like a perfect 'L' shape. What type of angle did Mason draw? Answer: right angle Solution: Visualize the corner of the room where two walls meet. This forms an angle. An 'L' shape has an opening that is exactly 90 degrees, which is called a right angle.
   Full step-by-step solution

   Step 1: Visualize the corner of the room where two walls meet. This forms an angle. Step 2: The problem says it looks like a perfect 'L' shape. Step 3: An 'L' shape has an opening that is exactly 90 degrees, which is called a right angle. Step 4: Therefore, the angle Mason drew is a right angle.

8. Noah is helping his teacher set up a geometry display in the school hallway. He needs to attach a long piece of string from one point on the wall to another point on the ceiling. The string will start at point A on the wall and go to point B on the ceiling, but it will not go beyond either point. Noah's friend asks if this string represents a line, a line segment, or a ray. What should Noah tell his friend? Answer: line segment Solution: Identify the properties of the string. The string starts at point A on the wall and ends at point B on the ceiling. It does not extend beyond either point.
   Full step-by-step solution

   Step 1: Identify the properties of the string. The string starts at point A on the wall and ends at point B on the ceiling. It does not extend beyond either point. Step 2: Compare to geometric definitions: - A line has no endpoints and goes forever in both directions. - A ray has one endpoint and goes forever in one direction. - A line segment has two endpoints. Step 3: Since the string has two endpoints (A and B), it matches the definition of a line segment. The answer is: line segment.