Lines and Angles

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Answer Key & Explanations

Lines and Angles · Grade 4 · Worksheet 1

1. Liam is drawing a large clock face on a piece of paper for his art project. He starts by drawing a point in the very center of the paper to mark the center of the clock. Then, he draws a straight line from the center point all the way to the edge of the paper to show the 12 o'clock mark. Next, he draws another straight line from the center point to the 3 o'clock mark. What type of angle is formed by the two lines Liam drew at the center point? Answer: right angle Solution: Liam draws one line from the center straight up to 12 o'clock. Step 2: He draws another line from the center straight to the right to 3 o'clock.
   Full step-by-step solution

   Step 1: Liam draws one line from the center straight up to 12 o'clock. Step 2: He draws another line from the center straight to the right to 3 o'clock. Step 3: The space between these two lines at the center point forms a corner. Step 4: On a clock, the 12 and 3 are exactly one-quarter of the clock face apart. Step 5: One-quarter of a full circle (360 degrees) is 90 degrees. Step 6: An angle that is exactly 90 degrees is called a right angle. The answer is a right angle.

2. What type of angle is 137°? Answer: obtuse angle Solution: Recall the types of angles. A right angle is exactly 90°. An acute angle is less than 90°.
   Full step-by-step solution

   Step 1: Recall the types of angles. A right angle is exactly 90°. An acute angle is less than 90°. An obtuse angle is greater than 90° but less than 180°. A straight angle is exactly 180°. Step 2: Compare 137° to 90°. Since 137° is greater than 90°, it is not acute or right. Step 3: Check if it is less than 180°. 137° is less than 180°, so it is not a straight angle. Step 4: Therefore, 137° is an obtuse angle. The answer is obtuse angle.

3. 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.

4. Tane is building a model sailboat for a school project. He draws a large straight line across his paper to represent the horizon. Then, he draws a line that starts at a point on the horizon and goes straight up, making a perfect square corner with the horizon. What type of angle is formed at the point where the vertical line meets the horizon? Answer: D. Right angle Solution: The horizon is a straight line. The vertical line meets it at a point. Step 2: A square corner means the two lines are perpendicular to each other.
   Full step-by-step solution

   Step 1: The horizon is a straight line. The vertical line meets it at a point. Step 2: A square corner means the two lines are perpendicular to each other. Step 3: A perpendicular intersection creates an angle that measures exactly 90 degrees. Step 4: In geometry, a 90-degree angle is called a right angle. The correct answer is Right angle.

5. Aroha is designing a large kite in the shape of a quadrilateral. She marks a point at each corner of the kite. She then draws a straight line from the top corner to the bottom corner, and another straight line from the left corner to the right corner. The two lines cross exactly at the center. At the point where they cross, four angles are formed. One of these angles is 45 degrees. What type of angle is this? Answer: acute angle Solution: Recall the types of angles. A right angle measures exactly 90 degrees. An acute angle measures less than 90 degrees.
   Full step-by-step solution

   Step 1: Recall the types of angles. A right angle measures exactly 90 degrees. An acute angle measures less than 90 degrees. An obtuse angle measures more than 90 degrees but less than 180 degrees. A straight angle measures exactly 180 degrees. Step 2: Compare 45 degrees to 90 degrees. Since 45 is less than 90, the angle is smaller than a right angle. Step 3: Therefore, an angle that is smaller than a right angle is called an acute angle. The answer is acute angle.

6. Sophia is designing a playground on a grid. She draws a line that starts at point A and goes through point B without ending. She then draws another figure that has two endpoints and includes all the points between them. What geometric terms describe the first figure Sophia drew and the second figure she drew? Answer: The first figure is a ray, and the second figure is a line segment. Solution: Identify the first figure. The description says 'starts at point A and goes through point B without ending.' This means it has one endpoint (point A) and extends forever in one direction. That is the definition of a ray.
   Full step-by-step solution

   Step 1: Identify the first figure. The description says 'starts at point A and goes through point B without ending.' This means it has one endpoint (point A) and extends forever in one direction. That is the definition of a ray. Step 2: Identify the second figure. The description says 'has two endpoints and includes all the points between them.' This means it has a definite start and end. That is the definition of a line segment. Step 3: The answer is: first figure is a ray, second figure is a line segment.