Kinds of angles · Martinとコード

Five names for every opening

You can measure angles. Now they get names — because saying “obtuse angle” is faster than “an angle somewhere between 90 and 180 degrees”.

The split is simple and stands on two landmarks: 90° (a right angle, a notebook corner) and 180° (a straight angle, a straight line).

Acute angle: smaller than 90°. A tip that pokes — a pencil point, the roof of a letter A.
Right angle: exactly 90°. A notebook corner, a door corner. It is marked with a little arc with a dot, or a square.
Obtuse angle: between 90° and 180°. More open than a corner — the back of a comfy armchair.
Straight angle: exactly 180°. The arms make one straight line — an open book laid on a table.
Full angle: 360°. A whole turn — a skate “360”.

Telling kinds of angles means having two fixed points in your eye: a corner (90°) and a straight line (180°). Everything else is “smaller than”, “between”, or “exactly”.

Tereza and Filip play a spotting game around the class. “The board corner?” — “Right!” — “Open scissors, just at the tips?” — “Acute!” — “The bench back, how it leans?” — “Obtuse!” Filip tries a trick: “The minute hand after half an hour?” Tereza draws: the hand turns half the clock face, from twelve to six… “One hundred and eighty. A straight angle!” Filip looks further and suddenly points at the clock in triumph: “And after a whole hour?” “Three hundred and sixty — a full angle. The hand is back, as if nothing happened.”

💡

No protractor? A paper corner is exactly 90°. Put it on the angle: if the angle peeks out from under the paper, it is obtuse; if it hides, it is acute.

How to sort an angle with no measuring

A spotting method — two questions and one look:

Question 1: Is it exactly a corner (90°)? Put a paper corner or a ruler on it. It sits exactly → right angle. In geometry it is marked with a little arc with a dot inside (or a small square).

Question 2: Is it exactly a straight line (180°)? Arms in one line, vertex in the middle → straight angle.

Look: where between the landmarks does it fall?

Narrower than a corner → acute (0° to 90°).
Between a corner and a straight line → obtuse (90° to 180°).
A whole turn → full (360°).

There are also angles between 180° and 360° — they look like “a bite from the outside”. They are called reflex and you will meet them later; for now it is enough to know that the world does not end after a straight angle.

Why do the names matter? In later lessons you will work out angles — and names are a fast check. If an obviously acute angle comes out 140°, the calculation is wrong. The name of an angle = an estimate packed into one word.

A memory trick at the end: acute cuts (a tip), obtuse does not cut (opened), a right angle is simply a right corner — in English it is called a right angle, a “correct angle”.

Sort the angles 35°, 90°, 145° and 180°

I go by the landmarks:

35° — smaller than 90 → acute. (A tip, it pokes.)
90° — exactly a corner → right. (Mark: an arc with a dot.)
145° — between 90 and 180 → obtuse. (An opened armchair.)
180° — exactly a straight line → straight.

Notice: I did not have to measure anything, just compare the number with two landmarks. Sorting is comparing.

Clock hands and kinds of angles

Between the numbers on a clock face there is 30° (you know that from the last lesson). What kind of angle do the hands make:

at 1:00 — 1 × 30 = 30° → acute,
at 3:00 — 3 × 30 = 90° → right,
at 5:00 — 5 × 30 = 150° → obtuse,
at 6:00 — 6 × 30 = 180° → straight.

All day kinds of angles take turns over your head. A clock is the best geometry textbook in the house.

Checking a calculation with the name of the angle

Jonáš drew an angle that is meant to be acute, and with a protractor he got 130°. Where is the mistake?

An acute angle must be under 90°. The number 130 does not belong there — but 180 − 130 = 50, and fifty is acute!

Jonáš read the wrong scale of the protractor (the trap from lesson fifteen). The name of the angle saved him: he knew what SHOULD come out, and the number did not match.

A habit worth having: first the kind of angle by estimate, then the number by measuring. If they do not match, measure again.

⚠️

A right angle is exactly 90° — not “about”. An angle of 89° is acute and 91° obtuse, even if they look like a corner. When on a drawing you see the mark of an arc with a dot (or a square), it is a guaranteed 90°; without the mark do not trust your eye.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

名前 the angle from the picture.

Practise the questions

On paper

Draw, put a paper corner on, write names.

Draw by eye one angle of each kind: acute, right, obtuse, straight. Check the right one with a paper corner and mark it with an arc with a dot.
Sort with no drawing: 12°, 90°, 91°, 179°, 180°, 360°. By each one write the kind.
Walk the flat and find at least two acute, two right and two obtuse angles. Write where you found them.
At which whole hours do the hands make an acute angle? List all the options between 1:00 and 6:00 (count 30° per hour).

Now you 💪

I can name five kinds of angles with their bounds in degrees.
I can sort an angle from a number without hesitating: 145° is obtuse, 35° acute.
I can spot the mark of a right angle on a drawing and I know that without it the eye is not enough.

✅

Done when: To every angle — drawn or given as a number — you give the right name and you use it as a fast check of measuring.

What to take from this lesson

There are two landmarks: 90° (a corner) and 180° (a straight line). The rest is comparing.
Acute < 90° < obtuse < 180°. Right is exactly 90°, straight exactly 180°, full 360°.
A right angle is marked with an arc with a dot or a square — the mark is certainty, the eye is not.
A paper corner is a pocket protractor for 90°.
The name of an angle works as a check of calculations and measuring: an acute one cannot come out 130°.