Using a protractor to measure angles

Using a protractor to measure angles

Using a protractor

A protractor is a semicircular tool with degrees marked from 0° to 180° around the edge. Most protractors have two scales running in opposite directions — that's the part most beginners get tripped up on.

Parts of a protractor

  • Centre point (or origin) — the small cross-hair or hole in the middle of the flat edge.
  • Baseline — the straight edge of the protractor, marked 0° and 180°.
  • Scale — the ring of numbers from 0° to 180°. Most protractors print one scale on the inside, one on the outside.

How to measure step by step

  1. Place the centre point of the protractor exactly on the vertex of the angle.
  2. Rotate the protractor so the baseline lies along one of the rays.
  3. Find which scale (inner or outer) reads 0 on that same ray. Use that scale for the answer.
  4. Follow the other ray to where it crosses the scale. The number there is the angle in degrees.

Choosing the right scale

The two scales count in opposite directions: one from left to right (inner), the other from right to left (outer). To pick the right one, always start with the ray that reads 0.

A safety check: think about the angle first.

  • Does it look acute? Then the answer should be less than 90. If your reading is bigger than 90, you picked the wrong scale.
  • Does it look obtuse? Then the answer should be between 90 and 180.

Worked example

Measure the angle of a slice of pizza cut into eighths.

  1. Place the centre on the tip of the slice (the vertex).
  2. Lay the baseline along one crust edge.
  3. The other crust edge crosses the inner scale at 45°.

Check: 45° is acute, and the slice does look narrower than a square corner. So 45° is right.

Protractor placed on a slice of pizza, measuring 45°

Common mistakes

⚠️ Centre not on the vertex. If the centre is off by even a tiny amount, the reading is wrong. Press the centre carefully onto the vertex before you rotate.

⚠️ Reading the wrong scale. Always check the type of angle first. Acute < 90°, obtuse > 90°.

⚠️ Ray too short. If the ray doesn't reach the scale, extend it with a ruler before measuring.

What's next

Try it out