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Lines and Angles

Grade 4 · Geometry · Worksheet 2

  1. Mere draws an angle that measures 142°. What type of angle is it? Answer: ______________
  2. Tane is helping his grandfather build a wooden fence in their backyard. He draws a plan on paper showing a straight line that starts at point A and goes through point B without ending in either direction. Then he draws another line that starts at point C and ends at point D. Finally, he draws a line that starts at point E and goes forever in one direction past point F. What geometric terms describe the three lines Tane drew in order? Answer: ______________
  3. Charlotte is drawing a diagram of a city intersection. She draws two roads that cross each other. At the intersection, she labels four angles. One angle is formed by a horizontal road and a vertical road. What type of angle is formed where a horizontal road meets a vertical road? Answer: ______________
  4. Emma is drawing a playground map for her school project. She draws a large angle at the corner of the slide structure. One side of the angle points straight to the east, and the other side points straight to the north. What type of angle did Emma draw? Answer: ______________
  5. Hana is drawing a large map of her neighborhood for a school project. She draws a street that starts at the library and continues straight past the school, never ending in either direction. On the same map, she draws a path that starts at the park and goes straight to the corner store, stopping there. Later, Hana adds a line that begins at the fire station and goes on forever in one direction toward the river. What geometric terms describe each of the three things Hana drew on her map? Answer: ______________
  6. Hana is looking at a street intersection from above. Two streets cross each other, and the corner of a park sits at the intersection. The path along the park's edge forms a 45-degree angle with one of the streets. What type of angle is the 45-degree angle? Answer: ______________
  7. Emma is drawing shapes on a piece of paper. She draws a figure that starts at one point and goes on forever in one direction. Then she draws another figure that has two endpoints and does not go on forever. What are the names of these two figures? Answer: ______________
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Answer Key & Explanations

Lines and Angles · Grade 4 · Worksheet 2

  1. Mere draws an angle that measures 142°. What type of angle is it? Answer: obtuse angle Solution: Recall the types of angles: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°). Compare 142° to these ranges. 142° is greater than 90° and less than 180°.
    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: Compare 142° to these ranges. 142° is greater than 90° and less than 180°. Step 3: Therefore, 142° is an obtuse angle. The answer is obtuse angle.

  2. Tane is helping his grandfather build a wooden fence in their backyard. He draws a plan on paper showing a straight line that starts at point A and goes through point B without ending in either direction. Then he draws another line that starts at point C and ends at point D. Finally, he draws a line that starts at point E and goes forever in one direction past point F. What geometric terms describe the three lines Tane drew in order? Answer: line, line segment, ray Solution: The first line Tane drew starts at point A, goes through point B, and does not end in either direction. This is a line because a line extends infinitely in both directions. Step 2: The second line starts at point C and ends at point D.
    Full step-by-step solution

    Step 1: The first line Tane drew starts at point A, goes through point B, and does not end in either direction. This is a line because a line extends infinitely in both directions. Step 2: The second line starts at point C and ends at point D. It has two endpoints, so it is a line segment. Step 3: The third line starts at point E and goes forever in one direction past point F. This is a ray because a ray has one endpoint and extends infinitely in one direction. Step 4: In order, the three figures are: line, line segment, ray. Answer: line, line segment, ray.

  3. Charlotte is drawing a diagram of a city intersection. She draws two roads that cross each other. At the intersection, she labels four angles. One angle is formed by a horizontal road and a vertical road. What type of angle is formed where a horizontal road meets a vertical road? Answer: Right angle Solution: Visualize a horizontal road running left to right. Step 2: Visualize a vertical road running straight up and down. Step 3: Where they cross, they form four angles.
    Full step-by-step solution

    Step 1: Visualize a horizontal road running left to right. Step 2: Visualize a vertical road running straight up and down. Step 3: Where they cross, they form four angles. Step 4: A horizontal line and a vertical line are perpendicular to each other. Step 5: Perpendicular lines always form angles that measure exactly 90 degrees. Step 6: An angle that measures exactly 90 degrees is called a right angle. The answer is right angle.

  4. Emma is drawing a playground map for her school project. She draws a large angle at the corner of the slide structure. One side of the angle points straight to the east, and the other side points straight to the north. What type of angle did Emma draw? Answer: right angle Solution: Identify the directions: east and north are perpendicular to each other. Perpendicular lines form a 90-degree angle. A 90-degree angle is called a right angle.
    Full step-by-step solution

    Step 1: Identify the directions: east and north are perpendicular to each other. Step 2: Perpendicular lines form a 90-degree angle. Step 3: A 90-degree angle is called a right angle. The answer is a right angle.

  5. Hana is drawing a large map of her neighborhood for a school project. She draws a street that starts at the library and continues straight past the school, never ending in either direction. On the same map, she draws a path that starts at the park and goes straight to the corner store, stopping there. Later, Hana adds a line that begins at the fire station and goes on forever in one direction toward the river. What geometric terms describe each of the three things Hana drew on her map? Answer: The first is a line, the second is a line segment, and the third is a ray. Solution: The street that starts at the library and continues straight past the school, never ending in either direction, has no endpoints. That is a line.
    Full step-by-step solution

    Step 1: The street that starts at the library and continues straight past the school, never ending in either direction, has no endpoints. That is a line. Step 2: The path that starts at the park and goes straight to the corner store, stopping there, has two endpoints (park and store). That is a line segment. Step 3: The line that begins at the fire station and goes on forever in one direction toward the river has one endpoint (fire station) and extends infinitely. That is a ray. Final answer: The first is a line, the second is a line segment, and the third is a ray.

  6. Hana is looking at a street intersection from above. Two streets cross each other, and the corner of a park sits at the intersection. The path along the park's edge forms a 45-degree angle with one of the streets. What type of angle is the 45-degree angle? Answer: acute angle Solution: Remember that a right angle measures exactly 90 degrees and looks like the corner of a square. Step 2: An acute angle is any angle that measures less than 90 degrees. Step 3: A 45-degree angle is less than 90 degrees.
    Full step-by-step solution

    Step 1: Remember that a right angle measures exactly 90 degrees and looks like the corner of a square. Step 2: An acute angle is any angle that measures less than 90 degrees. Step 3: A 45-degree angle is less than 90 degrees. Step 4: Therefore, a 45-degree angle is an acute angle.

  7. Emma is drawing shapes on a piece of paper. She draws a figure that starts at one point and goes on forever in one direction. Then she draws another figure that has two endpoints and does not go on forever. What are the names of these two figures? Answer: ray and line segment Solution: Identify the first figure. It starts at one point and goes on forever in one direction. Step 2: Identify the second figure.
    Full step-by-step solution

    Step 1: Identify the first figure. It starts at one point and goes on forever in one direction. That is called a ray. Step 2: Identify the second figure. It has two endpoints and does not go on forever. That is called a line segment. Step 3: The two figures are a ray and a line segment.