4th Grade · 4.MD.C.6

Measuring angles with a protractor in 4th grade

Measuring angles with a protractor is the 4th grade skill that turns the idea of degrees into a number your child can read. A protractor is a half-circle tool marked from 0 to 180 degrees. Your child learns to line it up, read the right scale and draw an angle of a given size.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

What it means, in plain words

An angle is the turn between two rays that share a starting point, called the vertex. Angles are measured in degrees, and a full turn is 360 degrees. A protractor shows half of that turn, from $0^\circ$ to $180^\circ$ .

Measuring angles with a protractor takes three steps. Put the center mark, a small hole or cross in the middle of the straight edge, on the vertex. Turn the protractor so its 0 line lies along one ray. Then follow the other ray out to the numbers and read the measure. Most protractors have two rows of numbers that run in opposite directions. Your child reads the row that starts at 0 on the first ray.

In 4th grade, your child also draws angles. To draw a $40^\circ$ angle, draw one ray and put the protractor's center on its starting point. Make a dot at 40 on the row that starts at 0, then join the dot to the vertex. Knowing a few angles by sight, such as $45^\circ$ (half a square corner) and $90^\circ$ (a square corner), helps a child spot a reading that cannot be right.

Your child should be able to:

Place the protractor's center on the vertex and its 0 line on one ray
Choose the correct one of the two rows of numbers
Measure an angle to the nearest whole degree, whichever way the angle faces
Draw an angle of a given size, such as $65^\circ$

Example

One ray of an angle lies on the 0 of the outer row of numbers. The other ray points to the mark labeled 70 on the outer row and 110 on the inner row. What does the angle measure?

The first ray starts at 0 on the outer row, so read the outer row.
On the outer row, the second ray points to 70.
The angle is narrower than a square corner, so 70 makes sense and 110 does not.
The angle measures $70^\circ$ .

Example

How do you draw an angle of $125^\circ$ ?

Draw a ray. Its starting point is the vertex.
Put the protractor's center on the vertex and its 0 line along the ray.
Find 125 on the row that starts at 0 on the ray, and make a dot there.
Join the dot to the vertex. The angle is wider than a square corner, as a $125^\circ$ angle should be.

Where children usually get stuck

Your child measures the tip of a pie slice, which is clearly narrower than a square corner, and writes $120^\circ$ instead of $60^\circ$ .
Each mark on a protractor carries two numbers, one from each row. The child read the row that starts at 0 on the other side.
What helps. Before measuring, ask whether the angle is smaller or bigger than a square corner. Then put a finger on the 0 that the first ray touches and count up along that row.
Your child lines up the bottom edge of the protractor with the ray, and the reading comes out a few degrees off.
The straight bottom edge looks like the place to line things up. On many protractors the 0 line sits a little above that edge, and the center is a small hole or cross.
What helps. Find the center mark and the 0 line together before measuring anything. Then measure the corner of a book, which should read $90^\circ$ .
Your child measures angles well when one ray lies flat along the bottom of the page but gets stuck when the angle is tilted or upside down.
When every practice angle has a flat bottom ray, the child learns to read a number off the page instead of lining up the turn. A tilted angle shows that the habit does not work.
What helps. Draw an angle on a sheet of paper and turn the paper to a new position several times. Measure the angle each time and see that the number stays the same.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
A starting ray is already shown on each protractor. Which diagram shows a $30^{\circ}$ angle from that ray?
A
B
C
D
Show the answer and how to solve it
The matching diagram is the one showing $30^{\circ}$ . Its terminal ray crosses the $30^{\circ}$ mark on the scale that begins at the starting ray, forming a narrow acute angle.
1. 1Look at the target measure: $30^{\circ}$ . Since $30^{\circ}$ is less than $90^{\circ}$ , the correct angle is acute — it should open only slightly from the starting ray, much less than a right angle.
2. 2To read each protractor, start at $0^{\circ}$ on the side of the starting ray (the horizontal ray pointing right) and count along that scale toward the terminal ray. The mark where the terminal ray crosses is the angle measure.
3. 3The $60^{\circ}$ diagram opens twice as far as $30^{\circ}$ — too large. The $90^{\circ}$ diagram is a right angle, far too wide. The $150^{\circ}$ diagram shows the supplementary angle $(180^{\circ}$ − $30^{\circ} = 150^{\circ})$ , which happens when the wrong scale is read. The $30^{\circ}$ diagram has its terminal ray crossing exactly the $30^{\circ}$ mark — a narrow, clearly acute angle.
Common mistake. A common mistake is reading the wrong scale on the protractor. The two scales add up to $180^{\circ}$ , so reading the outer scale instead of the inner gives the supplementary angle $(180^{\circ}$ − $30^{\circ} = 150^{\circ})$ . Always start at $0^{\circ}$ on the scale that lines up with the starting ray.
The idea underneath. The protractor has two scales because angles can open in two directions. Always start counting at $0^{\circ}$ on the scale aligned with your starting ray, and follow that scale toward the terminal ray.
2Warm-up
A student measured the angle shown on the protractor below and recorded the result. Select the statement that best describes the student's measurement.
$\displaystyle \text{Student's reading: } 150^\circ$
A
The angle measures $30^{\circ}$ . The student read the wrong scale.
B
The angle measures $145^{\circ}$ . The student misread the position by one tick mark.
C
The angle measures $140^{\circ}$ . The student misread the position by two tick marks.
D
The angle measures $150^{\circ}$ . The student is correct.
Show the answer and how to solve it
The angle measures $30^{\circ}$ , not $150^{\circ}$ . The student read the outer scale instead of the inner scale — a $120^{\circ}$ error. The correct statement is: "The angle measures $30^{\circ}$ . The student read the wrong scale."
1. 1Start by reading the protractor yourself. The angle's base ray points to the $0^{\circ}$ mark, so use the same scale (the inner scale). Follow the terminal ray to where it crosses that scale — it lands right on $30^{\circ}$ .
2. 2Now compare your reading to the student's claim. The student wrote $150^{\circ}$ , but the protractor shows $30^{\circ}$ — the two readings don't match, so the student made an error.
3. 3The wrong scale's reading at this position is $150^{\circ}$ . The student read the outer scale instead of the inner, getting $150^{\circ}$ instead of the correct $30^{\circ}$ .
4. 4The correct statement names the actual angle $(30^{\circ})$ and identifies the wrong-scale reading as the error.
Common mistake. A common mistake is reading the wrong scale of the protractor (inner vs. outer), which would give $150^{\circ}$ instead of $30^{\circ}$ . Always read the scale whose $0^{\circ}$ mark lines up with the angle's base ray.
The idea underneath. To check a protractor reading, find which $0^{\circ}$ mark lines up with the angle's base ray, then count up that same scale to where the terminal ray points. The inner and outer scales give different numbers — only one is correct for any given angle.
3Stretch
A student measured the angle below using a protractor and wrote this value:
$\displaystyle 135^\circ$
Select the statement that best describes the student's work.
A
The protractor's center is not on the vertex of the angle.
B
The $0^{\circ}$ line is not lined up with a side of the angle.
C
The student read the wrong scale on the protractor.
D
The student's placement and answer are correct.
Show the answer and how to solve it
The placement is correct, but the angle measures $45^{\circ}$ , not $135^{\circ}$ . The student read the wrong scale on the protractor.
1. 1First, examine the protractor placement. The center of the protractor is on the vertex of the angle, and the $0^{\circ}$ line is lined up along one side of the angle. The placement is correct.
2. 2The angle is acute — clearly smaller than a right angle — so its measure must be less than $90^{\circ}$ . Starting at $0^{\circ}$ on the side of the angle and following that same scale, the other side crosses at $45^{\circ}$ .
3. 3The student wrote $135^{\circ}$ . The $45^{\circ}$ and $135^{\circ}$ marks share the same tick, but they are on opposite scales. Because the angle is acute, the correct reading is $45^{\circ}$ . The student followed the scale running in the wrong direction and landed on $135^{\circ}$ instead.
Common mistake. A common mistake is reading from the scale that starts at $0^{\circ}$ on the far side of the protractor rather than the scale that starts at $0^{\circ}$ on the side of the angle. Both scales share the $45^{\circ}/135^{\circ}$ tick mark, so the only way to know which value is correct is to start at $0^{\circ}$ on a side of the angle and follow that same scale.
The idea underneath. A protractor has two scales running in opposite directions. To read an angle correctly, start at $0^{\circ}$ on a side of the angle and follow that same scale around to where the other side crosses. The number where the other side lands is only correct if you stay on the right scale.
4Stretch
Leo wants to draw a $65^{\circ}$ angle from the starting ray. The protractor below shows Leo's attempt.
Select the statement that best describes Leo's work.
A
Leo's angle measures $70^{\circ}$ , which is $5^{\circ}$ larger than the $65^{\circ}$ target.
B
Leo's angle matches the $65^{\circ}$ target.
C
Leo's angle measures $60^{\circ}$ , which is $5^{\circ}$ smaller than the $65^{\circ}$ target.
D
Leo's angle measures $115^{\circ}$ , found by subtracting the $65^{\circ}$ target from $180^{\circ}$ .
Show the answer and how to solve it
Leo drew a $70^{\circ}$ angle, which is $5^{\circ}$ larger than the $65^{\circ}$ target. The statement that correctly describes Leo's work is: "Leo's angle measures $70^{\circ}$ , which is $5^{\circ}$ larger than the $65^{\circ}$ target."
1. 1Look at the protractor. Find where Leo's second ray crosses the protractor scale. The second ray crosses at $70^{\circ}$ .
2. 2Compare Leo's angle to the target. Leo's angle is $70^{\circ}$ . The target was $65^{\circ}$ . Since $70^{\circ}$ is bigger than $65^{\circ}$ , Leo's angle is too large.
3. 3Find how much too large by subtracting:
4. 4Leo's angle is $5^{\circ}$ larger than the target. The correct description is the option that says: "Leo's angle measures $70^{\circ}$ , which is $5^{\circ}$ larger than the $65^{\circ}$ target."
Common mistake. A common mistake is jumping straight to $115^{\circ} (which$ is $180^{\circ}$ − $65^{\circ})$ without carefully reading where the second ray crosses the scale. Always start counting from $0^{\circ}$ on the same scale that begins at the starting ray.
The idea underneath. When checking someone else's angle, first read the actual angle from the protractor, then compare to the target. Both the size of the difference AND the direction (larger or smaller) matter.