Not every angle is the same

Liri had already measured lots of angles with the set square. But she noticed: some looked quite different.

Liri: “Some angles are sharp and narrow, others wide and flat. Do they have names too?”
Erklärus: “Yes – depending on how big the angle is in degrees, it gets its own name.”

📊 The five types of angle

Instead of drawing each type of angle separately and statically, we’ll try it out live – simply drag the slider:

🧭 Liri’s angle clock – experience the family of angles live
Angle α: 50°
Type of angle: —
An angle of 45° is…
an acute angle
an obtuse angle

📐 Measuring an angle – step by step

Method – with the set square
Erklärus: “Place the baseline of your set square exactly along one arm of the angle, with the centre point of the scale exactly on the vertex.”
Liri: “And then I read off where the second arm crosses the degree scale?”
Erklärus: “Exactly. Just make sure you count from the right side – that is why the protractor has a double scale, one starting from the left and one from the right.”
Line up the arm → vertex on the centre point → read off the degrees
🌌 Angles in the universe

The Earth’s axis is tilted by about 23° – an acute angle that gives us our seasons.
Satellite solar panels are often aligned at a right angle (90°) to the Sun.
A straight angle (180°) describes a completely straight flight path – without any change of course.

❌ Common mistake

An angle of exactly 90° is sometimes called “acute” because it looks small – but 90° is always a right angle, not an acute one!

Tip: only something smaller than 90° is acute – not “looking small”, but really below the 90° limit.

📐 Exercise 1
An angle of 120° is…
an acute angle
an obtuse angle
📏 Exercise 2
How many degrees is a straight angle?
🔄 Exercise 3
An angle of 270° is…
an obtuse angle
a reflex angle

Angles with names

Liri looked at her star map: at every crossing on her route she had to turn – but not every turn was the same.

Liri: “At this crossing I turn almost all the way round – that is a reflex angle. At the next one only very slightly – an acute one.”
Erklärus: “That is exactly how you read a route: not only HOW FAR you go, but also HOW SHARPLY you turn. With the names of the types of angle you can judge every change of course on your map straight away, without measuring every time.”
Liri: “Now I can give every change of course a name – not just a number of degrees. That brings me a good deal closer to home.”
“Types of angle: acute (under 90°), right (exactly 90°), obtuse (90°–180°), straight (exactly 180°), reflex (180°–360°).”
What you learned today
acute · right · obtuse · straight · reflex
under 90° · exactly 90° · 90°–180° · exactly 180° · 180°–360°
🌟

Chapter 35 mastered!

Liri can now name every angle that she measures with the set square.

Erklärus’s notebook – page 35:
“Types of angle: acute (0°–90°), right (90°), obtuse (90°–180°), straight (180°), reflex (180°–360°).”
← Back to overview 35 – Types of Angle