Reading a protractor

A protractor is a half circle whose straight angle at the centre is divided into 180 parts of 1°. On an unlabelled protractor, starting from the 0 mark at one end of the base, there is a long mark every 10°, and a medium mark 5° after each long mark, halfway to the next one. So you can count in 10s and 5s instead of every single degree.

The protractor in your geometry box has two sets of numbers: an inner scale and an outer scale. One goes up from right to left, the other from left to right, so you can measure from either end. At every mark the two numbers add up to 180: 30 sits with 150, 40 with 140, and so on.

To measure an angle directly:

• Put the centre of the protractor exactly on the vertex.
• Turn it so that one arm lies along the base line, through 0.
• Use the scale that starts at 0 on that arm, and read where the other arm crosses it.

You can also subtract. In your book, arms OT and OS cross the outer scale at 20 and 55. The angle between them holds 55 − 20 = 35 parts, so ∠TOS = 35°.

Spot the mistakes. The vertex must sit on the centre, not somewhere else on the base. One arm must lie through 0. And you must read the scale that starts at 0 on that arm. If an angle is clearly less than a right angle but you read 145°, you used the wrong scale: the right reading is 180 − 145 = 35°. A quick check: an angle smaller than a right angle must read less than 90°.