Lines and Angles

lessonbunny.com

Answer Key & Explanations

Lines and Angles · Grade 4 · Worksheet 3

1. Isabella draws an angle that measures 127°. What type of angle is it? Answer: obtuse angle Solution: Recall the definitions of angle types. An acute angle is less than 90°. A right angle is exactly 90°.
   Full step-by-step solution

   Step 1: Recall the definitions of angle types. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is greater than 90° but less than 180°. A straight angle is exactly 180°. Step 2: Compare 127° to these ranges. Since 127° is greater than 90° and less than 180°, it falls in the obtuse category. Step 3: Therefore, the angle is an obtuse angle. The answer is obtuse angle.

2. 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.

3. Identify the type of angle: 136° Answer: obtuse angle Solution: Recall that a right angle measures exactly 90°, an acute angle measures less than 90°, an obtuse angle measures more than 90° but less than 180°, and a straight angle measures exactly 180°.
   Full step-by-step solution

   Step 1: Recall that a right angle measures exactly 90°, an acute angle measures less than 90°, an obtuse angle measures more than 90° but less than 180°, and a straight angle measures exactly 180°. Step 2: The given angle is 136°. Since 136° is greater than 90° and less than 180°, it is an obtuse angle. The answer is obtuse angle.

4. 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.

5. Ava is drawing a large playground map on the sidewalk. She draws a line that starts at point P and goes forever in one direction past point Q. She labels the starting point P and draws an arrow at the other end. What geometric figure did Ava draw? Answer: ray Solution: Ava's figure starts at point P (a definite starting point). The figure goes through point Q and has an arrow at the other end, meaning it continues forever in that direction.
   Full step-by-step solution

   Step 1: Ava's figure starts at point P (a definite starting point). Step 2: The figure goes through point Q and has an arrow at the other end, meaning it continues forever in that direction. Step 3: A geometric figure with one endpoint and an arrow showing it goes forever in one direction is called a ray. The answer is ray.

6. Isabella is drawing a map of her town for a school project. She draws a straight line to represent Oak Street that starts at the post office and goes on forever in one direction past the library. Next, she draws a line to represent Elm Street that has two endpoints, one at the school and one at the park. Finally, she draws a line to represent Main Street that goes straight in both directions without any endpoints. What three geometric figures did Isabella draw, in order? Answer: ray, line segment, line Solution: The first line (Oak Street) starts at the post office and goes on forever in one direction past the library. This is a ray because a ray has one endpoint and extends infinitely in one direction.
   Full step-by-step solution

   Step 1: The first line (Oak Street) starts at the post office and goes on forever in one direction past the library. This is a ray because a ray has one endpoint and extends infinitely in one direction. Step 2: The second line (Elm Street) has two endpoints, one at the school and one at the park. This is a line segment because a line segment has two endpoints and includes all points between them. Step 3: The third line (Main Street) goes straight in both directions without any endpoints. This is a line because a line extends infinitely in both directions. Step 4: In order, the three geometric figures are: ray, line segment, line. Answer: ray, line segment, line

7. Olivia is drawing a map of her neighborhood. She draws a straight line that starts at the library and goes on forever in one direction past the school. She labels the starting point at the library. What geometric figure did Olivia draw: a line, a line segment, or a ray? Answer: ray Solution: Identify the key parts of what Olivia drew. She has a starting point at the library. Step 2: The line goes on forever in one direction past the school.
   Full step-by-step solution

   Step 1: Identify the key parts of what Olivia drew. She has a starting point at the library. This is an endpoint. Step 2: The line goes on forever in one direction past the school. This means it has only one endpoint and extends infinitely in one direction. Step 3: In geometry, a figure that has one endpoint and extends forever in one direction is called a ray. A line would have no endpoints, and a line segment would have two endpoints. Therefore, Olivia drew a ray.