How to Use a Protractor to Measure Angles — KS3 Maths

To measure an angle with a protractor, place the centre hole on the vertex, align the baseline with one arm of the angle, and read the scale where the other arm crosses the protractor. Always check whether your answer makes sense — acute angles are less than 90°, obtuse between 90° and 180°.

The parts of a protractor

A standard school protractor is a semicircle marked from 0° to 180°. It has:

Centre point (origin hole): placed on the vertex (corner) of the angle.

Baseline: the straight flat edge, aligned with one arm of the angle.

Inner scale: starts from 0° on the right and increases to 180° on the left.

Outer scale: starts from 0° on the left and increases to 180° on the right.

The two scales exist so that you can measure angles opening from either side. Choosing the correct scale is the key skill.

How to measure an angle — step by step

Step 1 — place the protractor correctly

Put the centre hole exactly on the vertex (the point where the two arms of the angle meet). The protractor's flat baseline should lie exactly along one of the arms of the angle.

Step 2 — choose the correct scale

Find where the baseline arm of the angle crosses the protractor. If it aligns with 0° on the right-hand side, read the inner scale (which increases left). If it aligns with 0° on the left-hand side, read the outer scale (which increases right).

Shortcut: always start counting from the 0° that aligns with your baseline arm.

Step 3 — read the angle

Follow the second arm of the angle out to where it crosses the scale you are reading. That number is the angle in degrees.

Step 4 — sense-check your answer

Acute angle: must be between 0° and 90°

Right angle: exactly 90°

Obtuse angle: must be between 90° and 180°

Straight line: exactly 180°

If your reading says 140° but the angle looks acute, you have read the wrong scale — subtract from 180° to find the correct reading.

Worked example 1 — measuring an acute angle

An angle appears to open to roughly a third of a right angle. The baseline arm aligns with 0° on the right-hand scale (inner scale). The second arm crosses the inner scale at 38°.

Sense-check: 38° < 90°, so this is an acute angle. ✓

Answer: 38°

Worked example 2 — measuring an obtuse angle

An angle opens wider than a right angle. The baseline arm aligns with 0° on the left-hand side (outer scale). The second arm crosses the outer scale at 127°.

Sense-check: 90° < 127° < 180°, so this is an obtuse angle. ✓

Answer: 127°

How to draw an angle with a protractor

Draw a straight line (this will be one arm of the angle).

Place the centre hole of the protractor on one end of the line.

Align the baseline with the line.

Find the required angle on the correct scale and make a small pencil mark at that point.

Remove the protractor. Draw a line from the vertex through the pencil mark.

Label the angle.

Worked example 3 — draw an angle of 65°

Since 65° < 90°, the angle is acute. Starting from the baseline on the right, count to 65° on the inner scale and mark the point. Draw the arm through the mark. The angle opens to the left and looks like roughly two-thirds of a right angle — a good visual check.

Worked example 4 — draw an angle of 145°

Since 90° < 145° < 180°, this is obtuse. Align the baseline on the left, read the outer scale to 145°, mark, and draw. The angle should look wider than a right angle but less than a straight line.

Measuring reflex angles (greater than 180°)

A standard semicircular protractor cannot measure reflex angles directly. Use this method:

Measure the non-reflex (smaller) angle at the same vertex.

Subtract from 360°: Reflex angle = 360° − non-reflex angle

Example: If the non-reflex angle at a vertex is 75°, the reflex angle is 360° − 75° = 285°.

Angle types summary

Angle type | Range
Zero angle | 0°
Acute | Greater than 0°, less than 90°
Right angle | Exactly 90°
Obtuse | Greater than 90°, less than 180°
Straight angle | Exactly 180°
Reflex | Greater than 180°, less than 360°
Full turn | Exactly 360°

Angles in the national curriculum

The DfE's KS3 mathematics programme of study requires pupils to draw and measure line segments and angles in geometric figures, and to apply the properties of angles including at a point and on a straight line. The statutory national curriculum for Key Stage 3 and 4 confirms that using a protractor accurately is a foundational skill for all subsequent geometry at GCSE, including circle theorems and constructions.

Common mistakes when using a protractor

Mistake | How it shows up | How to avoid it
Reading the wrong scale | 142° measured as 38° | Always start counting from the 0° aligned with your baseline
Centre hole not on the vertex | Inaccurate angle measurement | Double-check the hole is exactly on the corner before reading
Extending a short arm before measuring | Imprecise reading | Extend the arm with a ruler first so it crosses the scale clearly
Not doing a sense-check | Obtuse angles recorded as acute | Always decide first: is this angle acute, right, or obtuse?

Frequently asked questions

Why does a protractor have two scales?

The inner and outer scales allow you to measure angles opening from either direction without rotating the protractor. Starting from 0° on the right uses the inner scale; starting from 0° on the left uses the outer scale. Choosing the scale that begins at 0° where your baseline arm sits guarantees you read the correct value.

How do I measure a reflex angle with a standard protractor?

A semicircular protractor only shows 0° to 180°. To measure a reflex angle (greater than 180°), measure the non-reflex angle at the same vertex, then subtract from 360°. For example, if the non-reflex angle is 110°, the reflex angle is 360° − 110° = 250°.

How accurate should my angle measurements be?

At KS3, you are expected to measure angles to the nearest degree. In practice, a careful reading to within 1° or 2° is sufficient. Always align the baseline precisely with one arm and the centre hole exactly on the vertex — these two positioning errors cause most inaccuracies.

What if the arms of the angle are too short to reach the scale?

Extend both arms using a ruler and pencil before placing the protractor. The angle does not change when you extend the arms — only the rays (not their length) define the angle. Make sure your extended lines are accurate by using a ruler.

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