Angle Measurement

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Answer Key & Explanations

Angle Measurement · Grade 4 · Worksheet 1

1. A pizza is cut into 8 equal slices. If you take 3 slices and arrange them so their pointed ends meet at the center, what is the angle measure formed by the two outer edges of your pizza slices? Answer: 135° Solution: A full circle has 360 degrees. The pizza is cut into 8 equal slices, so each slice has 360 ÷ 8 = 45 degrees. With 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 360 ÷ 8 = 45 degrees. Step 3: With 3 slices, the total angle is 3 × 45 = 135 degrees. Step 4: When the pointed ends meet at the center, the angle between the two outer edges is exactly the sum of all three slice angles. The answer is 135°.

2. Matiu is helping his dad build a birdhouse. The roof of the birdhouse is a triangle. One angle of the triangle is 74 degrees and another angle is 52 degrees. What is the measure of the third angle in the triangle? Answer: 54 degrees Solution: The sum of all three angles in any triangle is always 180 degrees. Add the two known angles: 74 + 52 = 126 degrees. Subtract that sum from 180 to find the third angle: 180 - 126 = 54 degrees.
   Full step-by-step solution

   Step 1: The sum of all three angles in any triangle is always 180 degrees. Step 2: Add the two known angles: 74 + 52 = 126 degrees. Step 3: Subtract that sum from 180 to find the third angle: 180 - 126 = 54 degrees. The third angle measures 54 degrees.

3. Lily is designing a triangular garden bed for her school. One angle measures 45° and another angle measures 65°. What is the measure of the third angle in the triangular garden bed? Answer: 70 Solution: Recall the triangle angle sum property. The sum of the three interior angles in any triangle is always 180 degrees. Write down the known 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: Write down the known angles. First angle = 45 degrees Second angle = 65 degrees Let the third angle be x degrees. Step 3: Set up the equation using the angle sum property. 45 + 65 + x = 180 Step 4: Add the two known angles. 45 + 65 = 110 Step 5: Substitute into the equation. 110 + x = 180 Step 6: Solve for x by subtracting 110 from both sides. x = 180 - 110 x = 70 Step 7: State the answer. The third angle measures 70 degrees.

4. A clock shows 3:00. The hour hand points at the 3 and the minute hand points at the 12. What is the angle measure between the two clock hands? Answer: 90° Solution: A full circle on a clock is 360 degrees. There are 12 numbers equally spaced around the clock. The angle between each number is 360 ÷ 12 = 30 degrees.
   Full step-by-step solution

   Step 1: A full circle on a clock is 360 degrees. Step 2: There are 12 numbers equally spaced around the clock. Step 3: The angle between each number is 360 ÷ 12 = 30 degrees. Step 4: At 3:00, the hour hand is at 3 and the minute hand is at 12. Step 5: Count the number of spaces between 12 and 3: There are 3 spaces. Step 6: Multiply the number of spaces by the degrees per space: 3 × 30 = 90 degrees. The angle between the clock hands is 90°.

5. A farmer is planting corn in a rectangular field. The field has a length of 125.5 meters and a width of 84.2 meters. What is the perimeter of the field in meters? Answer: 419.4 meters Solution: Identify the formula for perimeter of a rectangle: Perimeter = 2 × length + 2 × width Substitute the given values: Perimeter = 2 × 125.5 + 2 × 84.2 Multiply: 2 × 125.5 = 251.0 Multiply: 2 × 84.2 = 168.4 Add the results: 251.0 + 168.4 = 419.4 Include the units: 419.4 meters The answer is 419.4…
   Full step-by-step solution

   Step 1: Identify the formula for perimeter of a rectangle: Perimeter = 2 × length + 2 × width Step 2: Substitute the given values: Perimeter = 2 × 125.5 + 2 × 84.2 Step 3: Multiply: 2 × 125.5 = 251.0 Step 4: Multiply: 2 × 84.2 = 168.4 Step 5: Add the results: 251.0 + 168.4 = 419.4 Step 6: Include the units: 419.4 meters The answer is 419.4 meters.

6. 180° - (35° + 85°) = ? Answer: 60° Solution: Calculate the sum inside the parentheses: 35° + 85° = 120° Subtract this result from 180°: 180° - 120° = 60° The answer is 60°.
   Full step-by-step solution

   Step 1: Calculate the sum inside the parentheses: 35° + 85° = 120° Step 2: Subtract this result from 180°: 180° - 120° = 60° The answer is 60°.

7. Emma is designing a triangular flag for her school's sports team. The flag has two angles that measure 48° and 72°. What is the measure of the third angle in Emma's flag? Answer: 60 Solution: We know that the sum of all three angles in any triangle is 180°. Add the two known angles: 48° + 72° = 120° Subtract this sum from 180° to find the missing angle: 180° - 120° = 60° The third angle measures 60°.
   Full step-by-step solution

   Step 1: We know that the sum of all three 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 missing angle: 180° - 120° = 60° The third angle measures 60°.