Types of Angles: Acute, Right, Obtuse, Reflex
Types of Angles: Acute, Right, Obtuse, Reflex
TL;DR
The six types of angles by measure are acute (under 90°), right (exactly 90°), obtuse (90° to 180°), straight (180°), reflex (180° to 360°), and full (360°). This article defines each type with a diagram, then covers the angle-pair relationships — complementary, supplementary, adjacent, and vertical — and the common mistakes.
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Last updated on June 9, 2026 9 min read
One Sweep of a Clock Hand Makes Every Angle There Is
Watch a clock's minute hand for one full hour and it passes through every angle a geometry course will ever name. A sliver past twelve is acute; a quarter-hour is a right angle; half past is straight; almost back to the top is a reflex angle. The hand does not jump between categories. It slides through them, and the types of angles are just the named stops along that one continuous sweep.
Knowing where each named stop sits is the whole skill, so we walk through them in order of size, then look at how angles pair up.
What Is an Angle?
An angle is the figure formed by two rays (called the arms or sides) that share a common endpoint (the vertex). The size of an angle measures the amount of turn between the two arms, recorded in degrees (°), where a full turn is 360°. We write an angle with the vertex letter in the middle: ∠ABC has its vertex at B.
The arms can be any length, short or long. Length does not change the angle. What matters is only the opening between them. That single idea, angle measures turn, not length, is what lets us sort every angle into a type by its degree measure alone.
The Types of Angles by Measure
Every angle falls into one of six named bands based on how many degrees it spans. This is the classification that exam questions ask about most.
| Type of angle | Measure | Everyday example |
|---|---|---|
| Acute angle | Greater than 0°, less than 90° | The tip of a slice of pizza |
| Right angle | Exactly 90° | The corner of a book |
| Obtuse angle | Greater than 90°, less than 180° | A reclining chair's back |
| Straight angle | Exactly 180° | A flat, opened-out ruler |
| Reflex angle | Greater than 180°, less than 360° | The larger opening of a wide-flung door |
| Full (complete) angle | Exactly 360° | One full spin of a wheel |
Definitions:
- An acute angle is sharp and narrow, smaller than a right angle. ∠ABC=30° is acute.
- A right angle is exactly 90° and is marked with a small square in the corner, not an arc. The two arms are perpendicular.
- An obtuse angle is wide and open, larger than 90° but still less than a straight line. ∠PQR=135° is obtuse.
- A straight angle is exactly 180°: the two arms point in opposite directions and form a straight line through the vertex.
- A reflex angle is the large angle, more than 180° but less than a full turn. Every angle below a straight angle has a reflex partner that completes the 360°.
- A full angle (or complete angle) is 360°: the arm has swept all the way back to where it started.
How Angles Pair Up — Complementary, Supplementary, Adjacent, Vertical
Beyond their individual size, angles are also classified by how they sit in relation to another angle. These pair-relationships are where most real problems live.
- Adjacent angles share a common vertex and a common arm, and sit side by side without overlapping.
- Complementary angles are two angles whose measures add to exactly 90°. If one is 30°, its complement is 60°.
- Supplementary angles are two angles whose measures add to exactly 180°. If one is 110°, its supplement is 70°.
- Vertical angles are the opposite pair formed when two lines cross. They are always equal.
A reader question that comes up constantly: what are the angles that add up to 90° and 180° called? The 90° pair is complementary; the 180° pair is supplementary. A common memory aid: C comes before S in the alphabet, and 90 comes before 180 — Complementary is the smaller sum.
Positive and Negative Angles
Angles also carry a direction of turn. An angle measured counter-clockwise from a starting arm is called positive; one measured clockwise is negative. This matters in trigonometry and in coordinate geometry, where the sign of the angle tells you which way the rotation went, not just how far. For most school geometry the angles are positive, but the convention is worth meeting early — you will pick it up again on the unit circle.
Examples of Types of Angles
With every type named, here is the classification in action. The problems build from naming a single angle up to using a pair relationship.
Example 1: Classify the angle ∠ABC=47°.
Since 47° is greater than 0° and less than 90°, the angle is acute.
Example 2: An angle measures 200°. A student labels it obtuse. Is that right?
A first instinct is "it is bigger than 90°, so it is obtuse." Check that against the bands. Obtuse stops at 180°; this angle is past a straight angle. Since 200° is greater than 180° and less than 360°, it is a reflex angle, not obtuse.
Example 3: Two angles are complementary. One measures 35°. Find the other.
Complementary angles add to 90°, so the other is 90°−35°=55°.
Example 4: Two angles are supplementary, and one is 124°. Find the other
Supplementary angles add to 180°, so the other is 180°−124°=56°.
Example 5: Two lines cross. One of the four angles is 73°. Find all four angles.
The angle vertically opposite is equal: 73°. Each of the other two is supplementary to 73° along a straight line: 180°−73°=107°. So the four angles are 73°, 107°, 73°, 107°.
Example 6: An angle is 130°. State its type and the measure of its reflex partner
130° is between 90° and 180°, so it is obtuse. Its reflex partner completes the full turn: 360°−130°=230°.
Why the Types of Angles Matter Beyond the Classroom
Naming angles is not busywork. Every field that builds, measures, or navigates depends on knowing an angle's type before doing anything with it.
- Construction and carpentry. A right angle is the foundation of every square corner; a frame that is even slightly acute or obtuse where it should be 90° will not sit true, and walls go out of plumb.
- Navigation and surveying. Bearings are angles measured from a fixed direction; whether a turn is acute or reflex changes the entire route. GPS and triangulation rest on measuring angles precisely.
- Design and engineering. Ramps, roofs, and camera mounts are specified by angle. A wheelchair ramp too steep (too large an angle from the ground) fails accessibility codes.
- Sport and physics. The angle a ball leaves a foot or a cue changes its whole path; reflex and obtuse angles describe overshoots and rebounds.
For a Grade 6 student, the types of angles are the alphabet of geometry: once you can name what you are looking at, every later topic — triangles, polygons, the transversal angle pairs — becomes a sentence built from these letters.
Where Students Trip Up on Types of Angles
Mistake 1: Calling a reflex angle obtuse
Where it slips in: An angle is clearly larger than a right angle, so the student stops checking and labels it obtuse.
Don't do this: Assume "bigger than 90°" automatically means obtuse.
The correct way: Obtuse lives strictly between 90° and 180°. Once an angle passes 180°, it is reflex. Always ask: has this angle crossed the straight-angle line?
Mistake 2: Swapping complementary and supplementary
Where it slips in: A problem says two angles "add up to" a number, and the student reaches for the wrong sum.
Don't do this: Use 180° when the problem is about a 90° pair, or vice versa.
The correct way: Complementary = 90° (the smaller word goes with the smaller sum, alphabetically C before S). Supplementary = 180°. Read which total the problem names before subtracting.
Mistake 3: Measuring an angle the wrong way around the vertex
Where it slips in: A protractor can read an angle two ways — the small arc or the large arc — and the second-guesser reads the wrong scale.
Don't do this: Read 130° as 50° by following the wrong row of numbers on the protractor.
The correct way: Decide first whether the angle is acute or obtuse by eye, then pick the protractor scale that matches. An obtuse-looking angle cannot read as 50°.
Key Takeaways
- The six types of angles by measure are acute, right, obtuse, straight, reflex, and full, sorted purely by degree.
- An angle's arms can be any length; only the turn between them sets its type.
- Angle pairs add structure: complementary sum to 90°, supplementary to 180°, vertical angles are equal, adjacent angles share a vertex and an arm.
- The most common mistake is calling a reflex angle (over 180°) "obtuse" — always check whether the angle has crossed the straight-angle line.
- Naming an angle correctly is the first step in every later geometry topic, from triangles to transversal angle pairs.
Practice These Problems to Solidify Your Understanding
- Classify each angle: 15°, 90°, 178°, 270°, 360°.
- Two angles are complementary; one is 62°. Find the other.
- An angle measures 145°. State its type and its reflex partner's measure.
Answer to Question 1: acute, right, obtuse, reflex, full. Answer to Question 2: 28°. Answer to Question 3: obtuse; reflex partner 215°.