Angles: amplitude, degrees, protractor and construction — 11–13
Measure an angle in degrees with a protractor, classify it, estimate it from 45°, 90° and 180°, and construct one.
The amplitude of an angle and the degree
The amplitude of an angle tells you how far one side has to turn around the vertex to reach the other. It is measured in degrees (°): a full turn is 360°, a half turn is 180° (a straight angle) and a quarter turn is 90° (a right angle). An acute angle is less than 90°; an obtuse angle is more than 90° and less than 180°. The length of the sides you drew does not matter: only the opening does.
Why we measure in degrees
To compare openings we need a measure everyone shares. One degree is 1/360 of a full turn. The number 360 is handy because it has many divisors (2, 3, 4, 5, 6, 8, 9, 10, 12…), so you can split a turn into equal parts using whole degrees: a quarter turn is 90° and an eighth is 45°. That is why 45°, 90° and 180° work as reference angles for estimating. And since the amplitude depends only on the opening, an angle can be measured on any sheet.
Measure, classify and construct an angle
Measure: put the protractor's centre on the vertex and its zero on one side. The other side crosses 130 on the outer scale and 50 on the inner one. The zero is on the outer scale, so the angle is 130°: obtuse. Check by eye first: it is wider than a right angle, so 50° cannot be right. Construct 65°: draw a ray from O, place the protractor, mark 65° on the scale that starts at that ray and join O to the mark. 65° is acute and nearer 45° (20° away) than 90° (25° away).
The trap: reading the wrong scale
A protractor has two scales, one growing to the right and the other to the left, and the classic mistake is to read the one that does not start at zero on your side. An obtuse angle read as 40° instead of 140° goes unnoticed if you do not estimate first. Always check: acute means under 90°, obtuse means over 90°. If the reading contradicts what you see, you swapped scales: the other one gives what is missing to 180° (40° + 140° = 180°).
Where you see this outside school
A clock has 12 marks and a full turn is 360°, so each hour is 30° (360 ÷ 12): at 3 o'clock the hands form 90° and at 6 o'clock they form 180°. When you tell a robot in a coding game to turn 90° to the right, you are giving an angle. A door that opens a quarter turn opens 90°. The opening of a laptop, of a pair of compasses or of scissors is also described in degrees.
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