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Angles: measuring, adding, recognising

Level 3 · Ages 11–13

Quick recall· Let's wake up what you already know before we start.

Recall: two rays starting from the same point form an angle. What is this point called?

The whole lesson

Read it again any time, including while you work through the exercises.

Open a pair of scissors: the wider you open it, the bigger the angle between the two blades. An angle is exactly that: the opening between two rays starting from the same point, the vertex. Careful, the length of the blades does not matter! Small scissors opened wide make a bigger angle than long scissors barely open.

To measure an angle, we use a protractor, graduated in degrees (°). The reference to know by heart: a right angle measures 90°, like the corner of a sheet of paper. An angle more closed than a right angle (less than 90°) is acute, like an arrowhead. An angle more open (between 90° and 180°) is obtuse. And if the two rays are perfectly aligned, the angle is straight: 180°.

To measure well, three moves: place the centre of the protractor exactly on the vertex, line up the zero with one side, then read the mark crossed by the other side. Pro tip: before reading, ask yourself whether the angle is acute or obtuse. If the angle clearly looks acute, its measure must be below 90°; this saves you from reading the wrong scale on the protractor!

Angles also add up: if two angles sit side by side around the same vertex, the total angle is the sum of both. And keep this treasure: in any triangle, the three angles always add up to 180°. It is one of the most beautiful rules in geometry.

The worked example, step by step

How do you measure an angle with a protractor?

  1. centre du rapporteur sur le sommet

    I place the small hole (or cross) of the protractor exactly on the vertex of the angle.

  2. zéro aligné sur un côté

    I rotate the protractor so the 0° mark lines up perfectly with one side of the angle.

  3. lecture sur l'autre côté : 55°

    I read the mark crossed by the other side, counting from zero: here 55. I check: the angle looks acute and 55 is indeed less than 90. Everything is consistent!

Result: The angle measures 55°.

Two angles sit side by side around the same vertex: one measures 40°, the other 35°. What is the total angle?

  1. angle total = 40° + 35°

    The two angles follow each other without overlapping: the total angle is the sum of both openings.

  2. 40 + 35 = 75

    I add the measures: 40 plus 35 equals 75. The total angle is 75°, still acute since it is below 90°.

Result: The total angle measures 75°.