Angle Measurement

Grade 4 · measurement · 79 practice problems · read aloud

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📐 Angle Measurement

An angle is the space between two lines that meet at a point (the vertex). We measure angles to describe how much something is turning or to compare the corners of shapes. It's super useful for building things, reading maps, and understanding shapes in math!

How to Measure an Angle

  1. Find the Vertex: Locate the corner point of the angle.
  2. Align the Protractor: Place the center hole of your protractor on the vertex. Line up one of the angle's sides with the 0° line.
  3. Read the Scale: Look where the other side of the angle crosses the number scale. Be careful to read from the correct set of numbers (0 to 180).

Visual Examples

Example 1: A Right Angle

This angle looks like a perfect corner. When you measure it, the second ray will point to 90 degrees. We use a little square in the corner to show this.

Example 2: An Acute Angle

This angle is smaller and sharper than a right angle. When you measure it, the number will be less than 90°, like 45° or 60°.

⚠️ Common Mistakes

  • Using the Wrong Numbers: Protractors have two rows of numbers. Always check if your angle is less than 90° (acute) to pick the smaller number, or greater than 90° (obtuse) to pick the larger number.
  • Wrong Center Point: The center hole of the protractor must be directly on the vertex of the angle.

💡 Tips & Tricks

  • Estimate First! Before measuring, ask: "Is this angle smaller than a square corner (90°) or larger?" This helps you pick the right scale.
  • Angle Animal Sounds: An A-cute angle is a small, cute angle (less than 90°). An O-btuse angle is a big, obese angle (more than 90°).

How to Practice

  • Use a protractor to measure the angles in your name written in "block letters."
  • Go on an Angle Hunt around your home or classroom. Find and sketch acute, right, and obtuse angles you see.
  • Draw your own angles and have a friend measure them to check your work!

Practice problems

6 of the 79, worked through step by step — try them before opening the answer.

1 124 × 3 = ?

Hint: Multiply each digit in the larger number by the smaller number, starting from the ones place, and remember to regroup if necessary.

Show the answer

Answer: 372

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

Let's multiply 124 by 3 step by step.

2 180° - 75° = ?

Hint: When you have a straight angle and know one part, you can find the other part by subtracting from the total.

Show the answer

Answer: 105°

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

3 180° - 45° = ?

Hint: When you subtract an angle from a straight angle, you're finding its supplement.

Show the answer

Answer: 135°

  1. We start with the problem: 180 degrees minus 45 degrees.
  2. Write this as a subtraction: 180° - 45°
  3. Subtract the numbers. First, subtract the ones place: 0 - 5. Since 0 is smaller than 5, we need to borrow from the tens place.
  4. The number 180 has 8 tens. We borrow 1 ten, which is 10 ones. The 0 in the ones place becomes 10, and the 8 in the tens place becomes 7.
  5. Now subtract the ones place: 10 - 5 = 5.
  6. Next, subtract the tens place: 7 (from 180 after borrowing) - 4 (from 45) = 3.
  7. Finally, subtract the hundreds place: 1 (from 180) - 0 (since 45 has no hundreds) = 1.
  8. Combine the results: 1 hundred, 3 tens, and 5 ones gives us 135.
  9. Remember to include the unit. Since we subtracted degrees,

the answer is 135 degrees. Therefore, 180° - 45° = 135°.

4 180° - (45° + 60°) = ?

Hint: First, add the two angle measures inside the parentheses. Then subtract that total from the full angle measure.

Show the answer

Answer: 75°

  1. Perform the addition inside the parentheses.** 45° + 60° = 105° **
  2. Substitute the result back into the expression.** 180° - 105° **
  3. Subtract 105° from 180°.** 180° - 105° = 75° **Final Answer:** 75°

Let's solve the problem step by step. We have: 180° - (45° + 60°) **

5 180° - (35° + 90°) = ?

Hint: Remember to perform the operations inside parentheses first before subtracting from 180 degrees.

Show the answer

Answer: 55°

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

The answer is 55°.

6 180° - (35° + 42°) = ?

Hint: Remember to solve what's inside the parentheses first before subtracting from 180 degrees.

Show the answer

Answer: 103°

  1. First, solve the addition inside the parentheses: 35° + 42° = 77°
  2. Now subtract this result from 180°: 180° - 77° = 103°

The answer is 103°.

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