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Angle Measurement

Grade 4 · Measurement · Worksheet 2

  1. A pizza is cut into 8 equal slices. If you take 3 slices and arrange them so their crust edges meet at the center, what is the angle measure at the center where the slices meet? Answer: ______________
  2. Lily is designing a quilt pattern using right triangles. One triangle has angles measuring 30° and 60°. What is the measure of the third angle in this triangle? Answer: ______________
  3. 180° - (35° + 45°) = ? Answer: ______________
  4. A rectangular garden has a length of 12.5 meters and a width of 8.4 meters. What is the perimeter of the garden in meters?
    Answer: ______________
  5. 180° - 75° = ? Answer: ______________
  6. Liam is building a rectangular garden bed that measures 12 feet long and 8 feet wide. He wants to put a decorative border around the entire garden. How many feet of border material does Liam need to buy?
    Answer: ______________
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Answer Key & Explanations

Angle Measurement · Grade 4 · Worksheet 2

  1. A pizza is cut into 8 equal slices. If you take 3 slices and arrange them so their crust edges meet at the center, what is the angle measure at the center where the slices meet? Answer: 135° Solution: A full circle has 360 degrees. The pizza is cut into 8 equal slices, so each slice has an angle of 360 ÷ 8 = 45 degrees at the center. If you take 3 slices, the total angle is 3 × 45 = 135 degrees.
    Full step-by-step solution

    Step 1: A full circle has 360 degrees. Step 2: The pizza is cut into 8 equal slices, so each slice has an angle of 360 ÷ 8 = 45 degrees at the center. Step 3: If you take 3 slices, the total angle is 3 × 45 = 135 degrees. Step 4: Therefore, the angle measure at the center where the 3 slices meet is 135 degrees.

  2. Lily is designing a quilt pattern using right triangles. One triangle has angles measuring 30° and 60°. What is the measure of the third angle in this triangle? Answer: 90° Solution: Recall the triangle angle sum property. The sum of the three interior angles in any triangle is always 180 degrees. Identify the given angles.
    Full step-by-step solution

    Step 1: Recall the triangle angle sum property. The sum of the three interior angles in any triangle is always 180 degrees. Step 2: Identify the given angles. The problem states the triangle has angles measuring 30° and 60°. Step 3: Let the third angle be x degrees. Using the triangle angle sum property: 30 + 60 + x = 180 Step 4: Add the known angles. 30 + 60 = 90 Step 5: Substitute into the equation. 90 + x = 180 Step 6: Solve for x. x = 180 - 90 x = 90 Step 7: State the conclusion. The measure of the third angle is 90 degrees. This makes sense because a triangle with angles 30°, 60°, and 90° is a right triangle, which matches the problem's description of using right triangles.

  3. 180° - (35° + 45°) = ? Answer: 100° Solution: Calculate inside the parentheses: 35° + 45° = 80° Subtract this result from 180°: 180° - 80° = 100° The answer is 100°.
    Full step-by-step solution

    Step 1: Calculate inside the parentheses: 35° + 45° = 80° Step 2: Subtract this result from 180°: 180° - 80° = 100° The answer is 100°.

  4. A rectangular garden has a length of 12.5 meters and a width of 8.4 meters. What is the perimeter of the garden in meters? Answer: 41.8 meters Solution: We are given a rectangular garden with length = 12.5 meters and width = 8.4 meters.
    Full step-by-step solution

    Step 1: Understand the problem We are given a rectangular garden with length = 12.5 meters and width = 8.4 meters. The perimeter of a rectangle is the total distance around the outside, which can be found using the formula: Perimeter = 2 × (length + width) Step 2: Add the length and width Length + width = 12.5 + 8.4 First, add the tenths place: 0.5 + 0.4 = 0.9 Then add the whole numbers: 12 + 8 = 20 So, 12.5 + 8.4 = 20.9 meters Step 3: Multiply by 2 Perimeter = 2 × 20.9 2 × 20 = 40 2 × 0.9 = 1.8 So, 40 + 1.8 = 41.8 meters Step 4: Final answer The perimeter of the garden is 41.8 meters.

  5. 180° - 75° = ? Answer: 105° Solution: We start with the problem: 180 degrees minus 75 degrees. Write the subtraction: 180 - 75. To subtract, we can break it down.
    Full step-by-step solution

    Step 1: We start with the problem: 180 degrees minus 75 degrees. Step 2: Write the subtraction: 180 - 75. Step 3: To subtract, we can break it down. First, subtract the tens: 180 - 70 = 110. Step 4: Now, subtract the remaining ones from the result. We need to subtract 5 more because 75 = 70 + 5. So, 110 - 5 = 105. Step 5: Therefore, 180 degrees minus 75 degrees equals 105 degrees. Final Answer: 105°

  6. Liam is building a rectangular garden bed that measures 12 feet long and 8 feet wide. He wants to put a decorative border around the entire garden. How many feet of border material does Liam need to buy? Answer: 40 Solution: To find how many feet of border material Liam needs, we need to calculate the perimeter of the rectangular garden bed. Identify the formula for the perimeter of a rectangle. The perimeter P of a rectangle is given by the formula: P = 2 * (length + width) Substitute the given measurements into…
    Full step-by-step solution

    To find how many feet of border material Liam needs, we need to calculate the perimeter of the rectangular garden bed. Step 1: Identify the formula for the perimeter of a rectangle. The perimeter P of a rectangle is given by the formula: P = 2 * (length + width) Step 2: Substitute the given measurements into the formula. The length is 12 feet and the width is 8 feet. So, P = 2 * (12 + 8) Step 3: Perform the addition inside the parentheses. 12 + 8 = 20 Step 4: Multiply the result by 2. P = 2 * 20 = 40 Step 5: State the final answer. Liam needs to buy 40 feet of border material.