Measuring Angles
Angles and their names
An angle measures the amount of turn between two arms meeting at a point called the vertex. Angles are named by their size. An acute angle is smaller than a right angle; a right angle is a square corner, marked with a small square; an obtuse angle is larger than a right angle but less than a straight line; a straight angle is a straight line; and a reflex angle is larger than a straight angle. Naming an angle is the first way to describe it, before any measuring, simply by comparing it to a right angle and a straight line.
Measuring angles in degrees
Angles are measured in degrees. A full turn, all the way around, is 360°, so a half turn, a straight angle, is 180°, and a quarter turn, a right angle, is 90°. The degree is the unit that gives every angle an exact size, so that two angles can be compared precisely rather than just by eye. Knowing these benchmarks, 90° for a right angle and 180° for a straight angle, anchors the whole scale and makes other angles easy to judge.
Estimating an angle
Before measuring, it is useful to estimate an angle by eye, using the benchmarks. An angle a little smaller than a square corner is around 60°; one a little larger, around 120°. Comparing an angle to a right angle of 90° and to a straight angle of 180° gives a sensible estimate, and estimating first is a good habit because it catches mistakes: a measurement far from the estimate is a sign that something has gone wrong. A good estimate is rarely exact, but it should be close.
Using a protractor
A protractor measures angles exactly. It is a half-circle marked from 0° to 180°. To measure an angle, the centre of the protractor is placed on the vertex and the zero line along one arm, and the size is read where the other arm crosses the scale. To construct an angle of a given size, the same setup is used in reverse, marking the point at the required degree and drawing the arm to it. Reading the correct scale, since most protractors have two, is the key to measuring accurately.
Naming angles from their size
Once an angle is measured, its size tells its name. An angle between 0° and 90° is acute; exactly 90° is a right angle; between 90° and 180° is obtuse; exactly 180° is a straight angle; and more than 180° is reflex. So an angle of 50° is acute, one of 130° is obtuse, and one of 200° is reflex. The name and the measure describe the same angle, one in words and one as a number, and moving between them shows a full understanding of the angle.
Working with angles confidently
Working with angles confidently means putting these skills together: name an angle by comparing it to a right angle and a straight line, measure it in degrees with a protractor, estimate its size first to check the measurement, and relate the degrees back to the name. The benchmarks of 90° and 180° guide both estimating and naming. With these habits a child can estimate, measure, construct and name any angle, ready for the geometry and the angle relationships of later years.