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Angle Measurement

Grade 4 · Measurement · Worksheet 3

  1. 180° - (65° + 45°) = ? Answer: ______________
  2. Lily is designing a rectangular garden with a length of 12 feet and a width of 8 feet. She wants to put a fence around the entire garden. What is the perimeter of Lily's garden?
    Answer: ______________
  3. Noah is building a triangular-shaped kite for a school project. He knows that two angles of the kite measure 48° and 72°. What is the measure of the third angle in Noah's kite? Answer: ______________
  4. 180° - 75° = ? Answer: ______________
  5. A triangle is drawn with angles measuring 65° and 45°. What is the measure of the third angle? Answer: ______________
  6. 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: ______________
  7. Emma is designing a triangular banner for her school fair. She knows that the sum of all angles in a triangle is 180 degrees. If one angle measures 75 degrees and another angle measures 42 degrees, what is the measure of the third angle in her banner? Answer: ______________
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Answer Key & Explanations

Angle Measurement · Grade 4 · Worksheet 3

  1. 180° - (65° + 45°) = ? Answer: 70° Solution: Calculate the sum inside the parentheses: 65° + 45° = 110° Subtract this sum from 180°: 180° - 110° = 70° The answer is 70°.
    Full step-by-step solution

    Step 1: Calculate the sum inside the parentheses: 65° + 45° = 110° Step 2: Subtract this sum from 180°: 180° - 110° = 70° The answer is 70°.

  2. Lily is designing a rectangular garden with a length of 12 feet and a width of 8 feet. She wants to put a fence around the entire garden. What is the perimeter of Lily's garden? Answer: 40 feet Solution: To find the perimeter of a rectangle, we use the formula: Perimeter = 2 × (length + width) Identify the length and width from the problem. Length = 12 feet Width = 8 feet Add the length and width.
    Full step-by-step solution

    To find the perimeter of a rectangle, we use the formula: Perimeter = 2 × (length + width) Step 1: Identify the length and width from the problem. Length = 12 feet Width = 8 feet Step 2: Add the length and width. 12 + 8 = 20 feet Step 3: Multiply the sum by 2. 2 × 20 = 40 feet Step 4: State the final answer. The perimeter of Lily's garden is 40 feet.

  3. Noah is building a triangular-shaped kite for a school project. He knows that two angles of the kite measure 48° and 72°. What is the measure of the third angle in Noah's kite? Answer: 60 Solution: Recall that the sum of all angles in any triangle is 180°. Add the two known angles: 48° + 72° = 120°. Subtract this sum from 180° to find the third angle: 180° - 120° = 60°.
    Full step-by-step solution

    Step 1: Recall that the sum of all angles in any triangle is 180°. Step 2: Add the two known angles: 48° + 72° = 120°. Step 3: Subtract this sum from 180° to find the third angle: 180° - 120° = 60°. The measure of the third angle is 60°.

  4. 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°

  5. A triangle is drawn with angles measuring 65° and 45°. What is the measure of the third angle? Answer: 70° Solution: Recall that the sum of all angles in any triangle is 180°. Add the two given angles: 65° + 45° = 110°. Subtract this sum from 180° to find the third angle: 180° - 110° = 70°.
    Full step-by-step solution

    Step 1: Recall that the sum of all angles in any triangle is 180°. Step 2: Add the two given angles: 65° + 45° = 110°. Step 3: Subtract this sum from 180° to find the third angle: 180° - 110° = 70°. The measure of the third angle is 70°.

  6. 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.

  7. Emma is designing a triangular banner for her school fair. She knows that the sum of all angles in a triangle is 180 degrees. If one angle measures 75 degrees and another angle measures 42 degrees, what is the measure of the third angle in her banner? Answer: 63 Solution: The sum of all angles in any triangle is 180 degrees. Add the two known angles: 75 + 42 = 117 degrees. Subtract this sum from 180 to find the third angle: 180 - 117 = 63 degrees.
    Full step-by-step solution

    Step 1: The sum of all angles in any triangle is 180 degrees. Step 2: Add the two known angles: 75 + 42 = 117 degrees. Step 3: Subtract this sum from 180 to find the third angle: 180 - 117 = 63 degrees. The third angle measures 63 degrees.