Angle Measurement

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Answer Key & Explanations

Angle Measurement · Grade 4 · Worksheet 3

1. A rectangular swimming pool is drawn with a length of 15 meters and a width of 8 meters. A straight rope is stretched diagonally from one corner of the pool to the opposite corner. What is the length of this diagonal rope? Answer: 17 Solution: The diagonal rope creates two right triangles within the rectangle. For a right triangle, the Pythagorean theorem states: a² + b² = c², where c is the diagonal (hypotenuse).
   Full step-by-step solution

   Step 1: The diagonal rope creates two right triangles within the rectangle. Step 2: For a right triangle, the Pythagorean theorem states: a² + b² = c², where c is the diagonal (hypotenuse). Step 3: The sides of the triangle are the length (15 m) and width (8 m) of the pool. Step 4: Calculate: 15² + 8² = 225 + 64 = 289 Step 5: Find the square root of 289: sqrt(289) = 17 Step 6: The diagonal rope is 17 meters long.

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. Olivia is measuring an angle with her protractor. She lines up one ray of the angle with the 0° mark on the protractor. The other ray crosses the protractor at the 117° mark. What is the measure of the angle? Answer: 117° Solution: Place the protractor's center on the vertex of the angle. Align one ray with the 0° mark on the protractor. Read the number where the second ray crosses the protractor's scale.
   Full step-by-step solution

   Step 1: Place the protractor's center on the vertex of the angle. Step 2: Align one ray with the 0° mark on the protractor. Step 3: Read the number where the second ray crosses the protractor's scale. The ray points to 117°. Step 4: Since one ray is at 0°, the angle measure is simply 117° - 0° = 117°. The angle measures 117°.

4. A rectangular swimming pool is drawn with a length of 15 meters and a width of 8 meters. A straight line is drawn from one corner of the pool to the opposite corner, creating two identical triangles. What is the area of one of these triangles? Answer: 60 Solution: Find the area of the entire rectangle using length × width Area of rectangle = 15 meters × 8 meters = 120 square meters The diagonal line divides the rectangle into two equal triangles Area of one triangle = 120 square meters ÷ 2 = 60 square meters The answer is 60 square meters.
   Full step-by-step solution

   Step 1: Find the area of the entire rectangle using length × width Area of rectangle = 15 meters × 8 meters = 120 square meters Step 2: The diagonal line divides the rectangle into two equal triangles Each triangle gets half of the rectangle's area Step 3: Calculate the area of one triangle Area of one triangle = 120 square meters ÷ 2 = 60 square meters The answer is 60 square meters.

5. 180° - (35° + 90°) = ? Answer: 55° Solution: Calculate the sum inside the parentheses: 35° + 90° = 125° Subtract this result from 180°: 180° - 125° = 55° The answer is 55°.
   Full step-by-step solution

   Step 1: Calculate the sum inside the parentheses: 35° + 90° = 125° Step 2: Subtract this result from 180°: 180° - 125° = 55° The answer is 55°.

6. Lily is designing a quilt pattern using triangular pieces. One triangular piece has angles measuring 45° and 65°. What is the measure of the third angle in this triangular quilt piece? Answer: 70 Solution: Recall the triangle angle sum property. The sum of the three interior angles in any triangle is always 180 degrees. Identify the two 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 two given angles. The problem states the triangle has angles of 45° and 65°. Step 3: Add the two given angles. 45 + 65 = 110 Step 4: Subtract the sum from 180 to find the third angle. Third angle = 180 - 110 = 70 Step 5: Conclusion. The measure of the third angle is 70 degrees. ANSWER: 70