Drawing and Measuring Angles with a Protractor

What a protractor measures

Angles are measured in degrees (°). A full turn is 360°, a half turn is 180°, and a right angle (a square corner) is 90°. A protractor is the tool that measures and draws these angles.

A semicircular protractor has:

• A centre point or cross in the middle of the straight edge.
• A baseline (the straight edge) marked 0° at both ends.
• A curved scale running 0° to 180°, usually with two rows of numbers going opposite ways.

Measuring an angle: four steps

1. Centre on the vertex. Put the protractor's centre cross exactly on the angle's vertex (the point where the two arms meet).
2. Line up the baseline. Rotate the protractor so one arm of the angle lies along the 0° line.
3. Find the right scale. Look at the arm on the 0° line. Follow the row of numbers that starts at 0 on that arm, up and around to the second arm.
4. Read the number where the second arm crosses the scale. That is your angle.

Described diagram: picture an angle opening to the upper right. The protractor sits with its flat edge along the bottom arm, centre cross on the corner. The bottom arm points to 0 on the inner scale. The slanted arm cuts the curved scale at the 50 mark, so the angle is 50°.

The two-scale trap

The most common error is reading the wrong scale. Because there are two rows, the same point shows two numbers that add up to 180 (for example 50 and 130).

To decide which is right, first judge the angle by eye:

• Acute angle: smaller than a right angle → less than 90°.
• Obtuse angle: wider than a right angle → between 90° and 180°.

If an angle clearly looks sharp (acute) but you read 130°, you have used the wrong scale; the answer is 50°. Always sanity-check this way.

Worked example: measuring

An angle looks a little wider than a right angle. You line up the bottom arm with 0° on the inner scale. The top arm crosses at the mark that reads 35 on the outer scale and 145 on the inner scale. Since you lined up with the inner scale's 0, you follow the inner numbers: the angle is 145° — an obtuse angle, which matches how it looks. ✓

Drawing an angle

To draw an angle of, say, 40° at a point:

1. Use a ruler to draw a straight baseline with a vertex marked at one end.
2. Place the protractor's centre cross on the vertex, baseline along the 0° line.
3. Find 40° on the correct scale and make a small, neat dot next to that mark.
4. Remove the protractor and use a ruler to join the vertex to the dot.

You now have a 40° angle. The same method works for any angle up to 180°.

Activity: angle hunt

Draw five angles of your choice (for example 30°, 75°, 90°, 120°, 160°) on paper. Swap with a partner. Measure each other's angles with a protractor and label whether each is acute, right or obtuse. Compare answers — they should agree within a degree or two.

Where this connects

Accurate measuring underpins all geometry. Once you can measure, you can investigate the rules of angles and lines and check facts like the angles in a triangle adding up to 180°.