Grade 4 Measuring Angles with a Protractor

Visual Model 1

Question: What is the measure of the angle shown in blue?

• A. 45 degrees
• B. 30 degrees
• C. 60 degrees
• D. 90 degrees

Why it works: The baseline of the angle starts at \(0\degree\) on the right. Follow the second ray until it crosses the degree scale—it lines up perfectly with the 45-degree mark. The answer is \(\mathbf{45}\) degrees.

Answer: 45 degrees

Visual Model 2

Question: A student measures an angle with a protractor. The angle opens to the 120-degree mark. What type of angle is this?

• A. Acute angle
• B. Right angle
• C. Obtuse angle
• D. Straight angle

Why it works: An obtuse angle opens wider than a right angle (more than \(90\degree\)) but is not a straight line (less than \(180\degree\)). Since \(120\degree\) fits perfectly between these benchmarks, the answer is \(\mathbf{\text{obtuse}}\).

Answer: Obtuse angle

Example 1

Question: When using a protractor, you have two scale choices (inner and outer). If the angle is opened towards the right side of the protractor, which scale should you use?

• A. Always use the inner scale
• B. Use the outer scale
• C. Use the scale that starts at 180 on the side where the angle opens
• D. It does not matter which scale you use

1. The key to reading a protractor is to use the scale that starts at \(0\degree\) on the same side where your angle opens.
2. When an angle opens toward the right, that side shows \(0\degree\)—read the outer scale.
3. This matches where the angle is heading.
4. The answer is \(\mathbf{\text{use the outer scale}}\).

Answer: Use the outer scale

Example 2

Question: What is the measure of the angle shown?

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 90 degrees

1. One ray sits on the baseline at \(0\degree\), and the other ray points to the \(30\degree\) mark.
2. Since \(30\degree < 90\degree\), this is an acute angle.
3. The answer is \(\mathbf{30}\) degrees.

Answer: 30 degrees

Example 3

Question: Sam uses a protractor to measure an angle. The angle lines up exactly with the 90-degree mark. What type of angle is this?

• A. Right angle
• B. Straight angle
• C. Obtuse angle
• D. Acute angle

1. Whenever an angle measures exactly \(90\degree\), we call it a right angle.
2. It's one of the most important angles we measure because it appears everywhere—in book corners, window frames, and the letter L.
3. This angle aligns perfectly with \(90\degree\), so the answer is \(\mathbf{\text{right angle}}\).

Answer: Right angle

Problem 1

Question: A student drew an angle and measured it. She read 115 degrees on the outer scale. Is this reasonable?

• A. No, because 115 is less than 90 degrees
• B. Yes, because 115 is between 90 and 180 degrees
• C. No, because you cannot measure angles larger than 100 degrees
• D. Yes, only if the angle opens to the left

Why it works: \(115\degree\) is absolutely a reasonable angle measure because it's between \(90\degree\) and \(180\degree\)—this makes it obtuse, not acute. The student's reading is correct. The answer is \(\mathbf{\text{yes, because 115 is between 90 and 180 degrees}}\).

Answer: Yes, 115 is obtuse

Problem 2

Question: A student said this angle measures 173 degrees. Is she correct?

• A. Yes, the angle is close to 180 degrees
• B. No, the angle is much smaller, around 7 degrees
• C. Yes, all small angles are close to 180 degrees
• D. No, you cannot measure angles smaller than 30 degrees

Why it works: This angle is tiny—it opens just \(7\degree\) from the baseline. Reading \(173\degree\) would be confusing the inner and outer scales. A common mistake is to read the wrong scale when an angle is very small or very large. The answer is \(\mathbf{\text{no, about 7 degrees}}\).

Answer: No, about 7 degrees