Types of angles and their names

Angles are named by size. An acute angle measures between 0 and 90 degrees, a right angle is exactly 90, an obtuse angle sits between 90 and 180, a straight angle is 180, a reflex angle is more than 180, and a full turn is 360. Two angles are complementary if they total 90 and supplementary if they total 180.

Veröffentlicht am 22. Juli 2026 · Quelle: Angle classifications, Elementary College Geometry, Mathematics LibreTexts

The names exist because size changes what an angle means. A carpenter hearing obtuse knows the joint opens out. A machinist hearing acute knows a cutter has to reach into a narrow corner. The vocabulary is small, it takes five minutes to learn properly, and it removes most of the ambiguity from a spoken instruction.

The definitions below follow the wording used in the LibreTexts college geometry text, which matches the standard school definitions in the UK, the US, and most other systems. There is very little variation between countries here, which is unusual and convenient.

What are the six types of angles?

Acute, right, obtuse, straight, reflex, and the full turn. They divide the whole range from 0 to 360 degrees into named bands, with the right angle and the straight angle marking the exact boundaries at 90 and 180. Every angle you will ever measure falls into one of these six.

• Acute angle: greater than 0 and less than 90 degrees. A sharp corner. The point of a triangle, a knife bevel, a roof gable.
• Right angle: exactly 90 degrees. A square corner. Marked with a small square rather than an arc.
• Obtuse angle: greater than 90 and less than 180 degrees. An open corner, like the interior angle of a hexagon at 120 degrees.
• Straight angle: exactly 180 degrees. The two arms form one straight line through the vertex.
• Reflex angle: greater than 180 and less than 360 degrees. The angle measured the long way round the outside.
• Full turn, also called a complete angle: exactly 360 degrees. One whole rotation back to the start.

Two boundary cases catch people out. Exactly 90 degrees is a right angle and nothing else, so it is neither acute nor obtuse. Exactly 180 degrees is a straight angle and not a reflex angle, since reflex begins above 180. Test questions love those two edges, and so do specifications, where writing 90 degrees or less is very different from writing less than 90 degrees.

There is also a zero angle, where the two arms lie on top of each other and the measure is 0 degrees. It rarely gets named in school work, but it appears constantly in engineering, where a shaft at 0 degrees and a shaft at 360 degrees are in the same position and mean different things about how it got there.

What are complementary and supplementary angles?

Two angles are complementary when their measures add up to 90 degrees, and supplementary when they add up to 180. So 30 and 60 are complementary, and 30 and 150 are supplementary. The angles do not have to touch each other or appear in the same diagram for the relationship to hold.

Both relationships do real work. In a right triangle, the two non-right angles are always complementary, because the three angles total 180 and one of them has taken 90. That is why measuring one acute angle in a right triangle gives you the other for free, by subtraction. It is the fastest cross check available on any square cornered layout.

Supplementary angles show up as soon as a line crosses another line. Angles on one side of a straight line at a point always total 180, so a 65 degree cut leaves a 115 degree remainder. That is the arithmetic behind every mitre: the joint angle and the cut angle are two halves of a supplementary pair.

Two more named pairs are worth carrying. Adjacent angles share a vertex and one arm, sitting side by side with no overlap. Vertically opposite angles are the pair facing each other where two straight lines cross, and they are always equal. Together with the 180 degree rule, those three facts solve most diagrams without measuring anything.

How do you mark and name angles correctly?

Mark an ordinary angle with a small arc drawn between the two arms, close to the vertex, and write the measure beside it with a degree symbol. Mark a right angle with a small square in the corner instead of an arc. Name an angle with three letters, putting the vertex in the middle, as in angle ABC.

• Single arc between the arms: an ordinary angle. Label it with the size, for example 47 degrees, or with a letter.
• Small square at the vertex: a right angle, exactly 90 degrees. Never draw an arc as well, the square already says it.
• Matching numbers of arcs on different angles: those angles are equal to each other. Two arcs each means equal, three arcs each means a third equal pair.
• Tick marks across lines: equal lengths, not angles. Easy to confuse on a crowded drawing.
• Arrowheads on lines: those lines are parallel. Matching arrowheads mark matching parallel sets.
• Three letter naming, angle ABC: the vertex is always the middle letter, B. Angle ABC and angle CBA are the same angle.

The three letter convention matters more than it seems. In a diagram with several angles at one point, writing angle B is ambiguous because there are three or four candidates. Angle ABC names exactly one of them. On any drawing that another person will read, spend the extra two letters.

For reflex angles, draw the arc all the way round the outside so the reader can see which side you mean. An arc drawn on the inside with 290 degrees written next to it is a contradiction, and someone will build the wrong thing. The arc, not the number, is what people look at first.

Where does each type show up in real work?

Right angles dominate building, because gravity and rectangular sheet materials both push that way. Acute angles appear on cutting edges and roof gables. Obtuse angles show up in polygon frames and shallow slopes. Reflex angles appear whenever you measure round the outside of a shape, such as an external corner of a room.

A concrete example of the reflex case: an external corner where two walls meet at 90 degrees on the inside presents 270 degrees on the outside, and skirting board or coving wrapping that corner has to be cut for the 270, not the 90. Getting the two mixed up is one of the classic trim mistakes, and it wastes a length of moulding every time.

Obtuse angles carry more of the load than people expect. The interior angle of a regular hexagon is 120 degrees and of a regular octagon is 135, so anything built from those shapes, from paving to hex nuts to quilt blocks, is an obtuse world. When you cut those joints, though, you set the saw to the acute complement, which is where the confusion starts.

What are the most common angle mistakes?

Reading the wrong scale on a double numbered protractor, which turns 60 into 120. Measuring the acute angle when the drawing wanted the reflex one. Assuming a sketch is drawn to scale. And treating the square corner symbol as decoration rather than a statement that the angle is exactly 90.

• The 60 and 120 swap. Before you write a reading down, ask whether the angle looks sharper or wider than a square corner, and check your number against that.
• Measuring inside when the job wanted outside. An external corner is 360 minus the internal angle, so 90 inside is 270 outside.
• Trusting a sketch. Unless it says to scale, the drawn angles mean nothing and only the labelled numbers count.
• Ignoring the right angle square. If a diagram marks a corner square, that angle is exactly 90 and you should not measure it, you should use it.
• Adding a reflex angle to its own arc. A shape total of 360 already includes the reflex portion, so counting it twice throws every later calculation out.

The sanity check that catches nearly all of these takes two seconds. Compare the angle to a right angle by eye before reading it. Sharper than square means the answer is below 90. Wider than square but still a single corner means between 90 and 180. Opening back on itself means reflex. If your number and your eye disagree, the number is wrong.