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Angle Measurement

Grade 4 · Measurement · Worksheet 1

  1. 180° - (65° + 42°) = ? Answer: ______________
  2. 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 hands? Answer: ______________
  3. Emma is designing a triangular flag for her school's sports team. The flag has one angle that measures 48° and another angle that measures 72°. What is the measure of the third angle in Emma's flag? Answer: ______________
  4. 124 × 3 = ? Answer: ______________
  5. Liam is designing a triangular kite for a school project. He measures two angles of the triangle and finds they are 52° and 78°. What is the measure of the third angle in Liam's kite? Answer: ______________
  6. 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: ______________
  7. Liam is building a triangular picture frame for his art project. He measures two angles of the triangle and finds they are 85° and 55°. What is the measure of the third angle in Liam's picture frame? Answer: ______________
  8. Liam is building a triangular picture frame for his art project. He measures two angles of the triangle and finds they are 52° and 78°. What is the measure of the third angle in Liam's picture frame? Answer: ______________
  9. Noah is building a triangular-shaped wooden frame for a school art project. He measures two angles of the triangle and finds they are 48° and 72°. What is the measure of the third angle in Noah's wooden frame? Answer: ______________
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Answer Key & Explanations

Angle Measurement · Grade 4 · Worksheet 1

  1. 180° - (65° + 42°) = ? Answer: 73° Solution: Add the angles inside the parentheses: 65° + 42° = 107° Subtract this sum from 180°: 180° - 107° = 73° The answer is 73°.
    Full step-by-step solution

    Step 1: Add the angles inside the parentheses: 65° + 42° = 107° Step 2: Subtract this sum from 180°: 180° - 107° = 73° The answer is 73°.

  2. 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 hands? Answer: 90° Solution: A full circle has 360 degrees. A clock face is divided into 12 equal sections (the hours). To find the angle between each hour, divide 360 by 12: 360 ÷ 12 = 30 degrees.
    Full step-by-step solution

    Step 1: A full circle has 360 degrees. Step 2: A clock face is divided into 12 equal sections (the hours). Step 3: To find the angle between each hour, divide 360 by 12: 360 ÷ 12 = 30 degrees. Step 4: At 3:00, the hour hand is at the 3 and the minute hand is at the 12. They are 3 sections apart (12 to 1, 1 to 2, 2 to 3). Step 5: Multiply the number of sections by the degrees per section: 3 × 30 = 90 degrees. The angle between the hands is 90°.

  3. Emma is designing a triangular flag for her school's sports team. The flag has one angle that measures 48° and another angle that measures 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 always 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 always 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°.

  4. 124 × 3 = ? Answer: 372 Solution: Write the multiplication vertically for clarity. 124 × 3 Multiply the ones place. 3 × 4 (ones) = 12 Write down 2 in the ones place, carry over 1 to the tens place.
    Full step-by-step solution

    Let's multiply 124 by 3 step by step. Step 1: Write the multiplication vertically for clarity. 124 × 3 Step 2: Multiply the ones place. 3 × 4 (ones) = 12 Write down 2 in the ones place, carry over 1 to the tens place. Step 3: Multiply the tens place. 3 × 2 (tens) = 6 Add the carried over 1: 6 + 1 = 7 Write down 7 in the tens place. Step 4: Multiply the hundreds place. 3 × 1 (hundreds) = 3 Write down 3 in the hundreds place. Step 5: Combine the digits. Hundreds: 3, Tens: 7, Ones: 2 So the result is 372. Final answer: 372

  5. Liam is designing a triangular kite for a school project. He measures two angles of the triangle and finds they are 52° and 78°. What is the measure of the third angle in Liam's kite? Answer: 50° Solution: The sum of all angles in a triangle is always 180°. Add the two known angles: 52° + 78° = 130° Subtract the sum of the known angles from 180°: 180° - 130° = 50° The third angle measures 50°.
    Full step-by-step solution

    Step 1: The sum of all angles in a triangle is always 180°. Step 2: Add the two known angles: 52° + 78° = 130° Step 3: Subtract the sum of the known angles from 180°: 180° - 130° = 50° Step 4: The third angle measures 50°.

  6. 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.

  7. Liam is building a triangular picture frame for his art project. He measures two angles of the triangle and finds they are 85° and 55°. What is the measure of the third angle in Liam's picture frame? Answer: 40° Solution: We know that the sum of all three angles in any triangle is always 180°. Add the two known angles: 85° + 55° = 140° Subtract this sum from 180° to find the missing angle: 180° - 140° = 40° The third angle measures 40°.
    Full step-by-step solution

    Step 1: We know that the sum of all three angles in any triangle is always 180°. Step 2: Add the two known angles: 85° + 55° = 140° Step 3: Subtract this sum from 180° to find the missing angle: 180° - 140° = 40° The third angle measures 40°.

  8. Liam is building a triangular picture frame for his art project. He measures two angles of the triangle and finds they are 52° and 78°. What is the measure of the third angle in Liam's picture frame? Answer: 50° Solution: We know that the sum of all angles in any triangle is 180°. Add the two given angles: 52° + 78° = 130°. Subtract this sum from 180° to find the third angle: 180° - 130° = 50°.
    Full step-by-step solution

    Step 1: We know that the sum of all angles in any triangle is 180°. Step 2: Add the two given angles: 52° + 78° = 130°. Step 3: Subtract this sum from 180° to find the third angle: 180° - 130° = 50°. The third angle measures 50°.

  9. Noah is building a triangular-shaped wooden frame for a school art project. He measures two angles of the triangle and finds they are 48° and 72°. What is the measure of the third angle in Noah's wooden frame? Answer: 60 Solution: Recall that the sum of all three angles in any triangle is always 180°.
    Full step-by-step solution

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