An angle is just an amount of turn — and its size tells you exactly what to call it. Grab the arm, swing it around, and watch the label change.
Start herePicture a door swinging open, or the hands of a clock spreading apart. The amount of turn between two arms — that's the angle. And here's the neat part: its size hands it a name, all on its own.
Open the door barely a crack and you've got a small, sharp angle. Swing it to a perfect square corner and you've got another kind. Push it flat against the wall, or all the way around — each amount of turn earns a different label. There are five names worth knowing: acute, right, obtuse, straight and reflex. By the end of this page you'll be able to glance at any angle and name it without thinking — and you'll have a protractor you can swing with your own hands to prove it.
Every angle is built from the same two parts. There's a single point where things meet — the vertex (that's just the fancy word for the corner). And there are two straight lines spreading out from it, called the arms of the angle. The angle itself is the opening between those two arms — how far one has turned away from the other. Think of opening your mouth: your jaw is the vertex, your top and bottom lips are the arms, and the angle is how wide you've opened.
We measure that opening in degrees, written with a little circle: 90°, 180°, and so on. Where does the scale come from? Imagine spinning all the way around on the spot, back to where you started — one full turn. That complete spin is split into 360 equal slices, and each slice is one degree. So a full turn is 360°. Halfway around — turning to face directly behind you — is half of that, 180°. And a quarter-turn, the crisp square corner you'd make turning from facing forward to facing sideways, is 90°.
Hold onto those three numbers — 90°, 180° and 360° — because they're the fence posts. Every angle's name comes from where it sits compared to them. Smaller than a quarter-turn, exactly a quarter, past a quarter but under a half, exactly a half, or bigger than a half: that's the whole classification, and you're about to feel it move.
This is the heart of the page, so play with it properly. Below is a full-circle protractor — think of it as two of your classroom protractors snapped together, so the arm can swing all the way around past 180°. One arm stays put, pointing right. Grab the other arm and drag it in a circle. As you do, the readout shows two things at once: the exact degrees of the opening, and the name of the type you've landed on.
Prefer not to drag? Use the slider, or click into the protractor and nudge the arm with your arrow keys. Try to land it exactly on the marked 90° (it gives a little snap) and watch the corner turn into a small square — the official "this is a right angle" badge. Then push past 180° into the giant reflex zone and see the wedge swallow more than half the circle.
Acute means sharp — any angle under 90°.
The type is read straight from the live degree value, so it's always correct: under 90° acute, exactly 90° right, 90–180° obtuse, exactly 180° straight, over 180° reflex.
Now let's pin each name to its exact range. Notice the pattern: two of the types are single, special values (the right angle at 90° and the straight angle at 180°), and the other three are the stretches of turn in between and beyond. The size is the type — there's nothing to memorise beyond where 90° and 180° sit.
A sharp, narrow opening — anything bigger than 0° but smaller than a square corner. Think of a slim pizza slice or the letter V.
A perfect square corner — a quarter-turn. It gets its own badge: a tiny square drawn in the corner instead of a curved arc.
Wider than a square corner but not yet a flat line — a relaxed, leaning-back opening. A reclining beach chair makes one.
A half-turn: the two arms line up into one flat straight line. Spin to face directly behind you and that's the turn you've made.
The big one — more than a half-turn (but less than a full 360° turn). It's the large opening you'd sweep going the "long way around".
The right-angle squareMathematicians have one special drawing rule: a right angle is never marked with a curved arc like other angles. Instead it gets a tiny square tucked into the corner. So if you ever spot a little square in a corner, that's a silent way of saying "this is exactly 90°" — no number needed.
A classroom protractor is a flat half-disc with numbers running around its curved edge from 0° to 180°. Measuring an angle with it comes down to lining it up, then reading off — but there's one little trap that catches everybody at first, so let's clear it up now.
The steps are simple. Put the protractor's small centre mark right on the vertex of your angle. Lay the flat baseline along one arm. Then follow the other arm out to the edge and read the number where it crosses.
Here's the trap. Look closely and you'll see two rows of numbers — one counting up from the left (0, 10, 20 … 180) and one counting up from the right (180, 170, 160 … 0). They're called the outer and inner scales, and they exist so the protractor works whichever way your angle faces. The golden rule: use whichever scale starts at 0° on the arm you lined up. If your baseline arm sits on the 0° of the inner scale, read the inner numbers; if it sits on the outer 0°, read the outer. There's a built-in cheat too — a quick glance tells you if the angle is acute or obtuse, so if your reading says 150° but the angle clearly looks sharp, you've picked the wrong scale. Trust your eyes to catch it.
Two scales, one job: pick the row that reads 0° on the arm you lined up, then follow the other arm to its number.
Once you start naming angles, you can't stop spotting them. The clock on the wall is the friendliest place to start: every hour mark is a tidy 30° apart (because a full 360° circle split into 12 hours is 360 ÷ 12 = 30°), so the gap between the hour and minute hands counts up in neat steps.
The hour hand points to 3, the minute hand straight up to 12 — three hours apart, 3 × 30° = a perfect right angle, 90°. At 2 o'clock it's a 60° acute angle; at 4 o'clock, a 120° obtuse one.
Now the hands point in exactly opposite directions, one straight up and one straight down. They form a flat line: a straight angle, 180°.
A door barely ajar makes an acute angle. Swing it to square with the frame and it's a right angle. Fling it wide so it leans back past square and you've got an obtuse angle.
A single thin slice cut from a pizza is an acute angle. The giant piece left behind — almost the whole pie — opens more than halfway around: that's a reflex angle.
The same idea is hiding in a pair of opening scissors (acute creeping toward obtuse as you spread them), the corner of this screen and every book and tabletop (right angles, all 90°), the splay of a gymnast's "180" half-turn or a skateboarder's "360" full spin, and the V of a peace sign. Naming angles isn't a classroom-only trick — it's a lens you can point at almost anything.
Time to train your eye. Each round shows you one fresh angle with the degrees hidden — just the two arms and the wedge between them. Decide what type it is and tap your answer. You'll get instant feedback, the real degree value revealed, and a running score with a streak to beat. Watch for the right-angle square and the flat straight line — those two are giveaways once you know them.
This one trips up nearly everyone at first. When two angles open by the same amount but one is drawn with much longer arms, the long-armed one looks bigger — it takes up more of the page. But an angle measures turn, not length. It's about how far one arm has swung away from the other, and that's completely unaffected by how long you draw the arms. Stretch them to the edge of the room or shrink them to stubs: the opening, and therefore the type, never changes.
Drag the slider to grow and shrink the arms below. The lines get longer and shorter, but the measured angle — computed live from where the arms actually point — sits perfectly still at 40°. Still acute, every time.
"This angle has really long sides, so it must be a big angle — way bigger than that little one over there."
Arm length is just how far you drew the lines. The angle is the turn between them — change the length all you like, the turn stays put.
The degree value is measured from the actual arm directions — so you can see for yourself it never budges from 40°.
This time you've got the degrees, no picture. Just slot each one against the fence posts: under 90°, exactly 90°, between 90° and 180°, exactly 180°, or over 180°. Decide each answer in your head first, then tap the card to flip it and check yourself.
Two of these are sneaky single values — 90° (right) and 180° (straight). The rest fall into a range.
An angle is the amount of turn between two arms, measured in degrees out of a full 360° spin.
Under 90° acute, exactly 90° right, 90–180° obtuse, exactly 180° straight, over 180° reflex.
Long or short arms don't change anything — only the opening between them sets the type.