Measuring Angles with a Protractor: Degrees, Setup, and Common Errors

Degrees and the 0°–180° Scale

A protractor measures angles in degrees, written with the symbol °. One full turn around a point is 360°, a straight line forms 180°, and a right angle is 90°. Most classroom protractors are semicircles, so their scale runs from 0° to 180°.

On a semicircular protractor, the numbers increase from 0 to 180 in one direction, and there is usually a second set of numbers that increases in the opposite direction. This is why choosing the correct scale matters: the same mark can represent two different measures depending on which side you start from.

Parts of a Protractor (What Each Part Does)

• Center point (or center hole/mark): the point you place exactly on the angle’s vertex.
• Baseline (or zero line): the straight edge along the bottom of the protractor. This must line up with one ray of the angle.
• Inner scale and outer scale: two number tracks. One starts at 0 on the left and increases to 180 on the right; the other starts at 0 on the right and increases to 180 on the left (the direction depends on the protractor design).
• Tick marks: small marks for each degree (often with longer marks at 5° and 10° intervals). These help you read accurately between labeled numbers.

Measuring an Angle: Precise Step-by-Step Procedure

Before you start

Make sure the rays are drawn clearly and meet at a sharp vertex. If the vertex is thick or messy, your reading can shift by several degrees.

Step 1: Place the center on the vertex

Put the protractor so its center point is exactly on the angle’s vertex. If your protractor has a hole, the vertex should sit in the middle of that hole.

Step 2: Align the baseline with one ray

Rotate the protractor until the baseline lies directly on top of one ray (or as close as possible). The ray should pass through the 0° line along the baseline, not above or below it.

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Step 3: Choose the correct scale (inner or outer)

Look at the ray you aligned with the baseline and find which 0° it matches (left-side 0 or right-side 0). Use the scale that starts at that 0°.

• If the baseline ray points to the left and matches the left 0°, you will typically read the scale that increases left-to-right.
• If the baseline ray points to the right and matches the right 0°, you will typically read the scale that increases right-to-left.

Step 4: Read where the second ray crosses

Without moving the protractor, find where the other ray intersects the protractor’s arc. Read the degree measure on the same scale you selected in Step 3.

Step 5: Record the measure clearly

Write the result with the degree symbol, for example m∠ = 47°. If your reading falls between labeled numbers, count tick marks carefully (each small tick is usually 1°).

Accuracy tip: avoid parallax

Look straight down at the protractor when reading the scale. Viewing from an angle can make the crossing point appear shifted.

Drawing an Angle of a Given Measure (Using a Protractor)

Goal

Given a vertex point and a starting ray, construct a second ray so the angle has the required degree measure.

Step-by-step

1. Draw a starting ray. Use a ruler to draw a straight ray from the vertex.
2. Place the protractor center on the vertex. Ensure the center mark is exactly on the vertex point.
3. Align the baseline with the starting ray. The starting ray should lie along the 0° line of one scale.
4. Choose the correct scale. Use the scale whose 0° sits on the starting ray.
5. Mark the target degree. Find the required measure (e.g., 25°) and make a small dot at that tick mark on the arc.
6. Draw the second ray. Remove the protractor and use a ruler to draw a ray from the vertex through the dot.
7. Label the angle measure. Write the degree measure near the angle.

Troubleshooting: Common Errors and How to Fix Them

1) Reading the wrong scale

Symptom: Your answer seems to be the “other number” at the same tick mark (for example, you read 140° when it should be 40°).

Fix: Always identify which 0° your baseline ray matches, then read from that scale. A quick check: if the angle looks small but you read a large number, you likely used the wrong scale.

2) Center not exactly on the vertex

Symptom: Re-measuring gives different results each time, or your measure is consistently off by several degrees.

Fix: Reposition the protractor so the center mark is precisely on the vertex. If the vertex is thick, use the sharpest point you can identify as the true intersection.

3) Baseline not aligned with the ray

Symptom: The reading changes when you slightly rotate the protractor; the ray is not sitting on the baseline.

Fix: Rotate the protractor until the ray lies exactly along the baseline (0° line). If needed, extend the ray lightly with a ruler so it reaches the baseline clearly.

4) Measuring the exterior angle by accident

Symptom: You get a measure that describes the “outside” opening rather than the intended interior opening (often close to 180° minus the expected value when using a semicircle protractor).

Fix: Decide which opening you are measuring before placing the protractor. If you intended the smaller opening but read a large number, re-check which side of the vertex you are measuring and which scale you used.

5) Starting from 10° or another number instead of 0°

Symptom: You accidentally begin counting from a labeled number that is not 0°, especially if the ray does not pass exactly through the 0° mark.

Fix: Ensure the baseline ray passes through the 0° mark. If it does not, realign the protractor; do not “count up” from a nearby number.

6) Confusing tick marks

Symptom: Off-by-1° to 5° errors, especially on angles like 25° or 135°.

Fix: Identify the 10° marks first, then count single-degree ticks carefully. If your protractor marks 5° intervals differently, use those as checkpoints.

Hands-on Practice: Measure, Record, Then Draw

Part A: Measure and record

Use a protractor to measure each angle below. Record your results in the table. (If you are working from a printed worksheet, measure the angles shown there. If you are creating your own angles, draw them first with a ruler and then measure.)

Instructions: Measure each angle twice (reposition the protractor each time). If the two measurements differ by more than 2°, check alignment and scale choice.

Part B: Draw specified angles

On blank paper, draw each angle from a starting ray. After drawing, measure your angle to verify.

• Draw an angle of 25°.
• Draw an angle of 90°.
• Draw an angle of 135°.

Verification table:

Self-Check: Is Your Answer Reasonable?

• Size check: Does the angle look smaller than a right angle? Then the measure should be less than 90°. Does it look larger than a right angle but less than a straight angle? Then the measure should be between 90° and 180°.
• Scale check: If you switch to the other scale at the same tick, the two readings add to 180° (for a semicircle protractor). If your answer seems wrong, see whether the other reading better matches the visual size.
• Alignment check: Reconfirm: center on vertex, baseline on one ray, and the second ray crossing is read on the chosen scale.
• Re-measure check: Measure again after lifting and replacing the protractor. Consistent results indicate correct setup; inconsistent results indicate misalignment or parallax.
• Drawing check: When drawing a target angle, your verification measurement should be close (typically within 1°–2°). Larger errors usually come from marking the wrong tick or using the wrong scale.