Types of Angles
Angles are grouped by how wide they open. Learn the six types by size, then the common angle pairs you will meet in geometry class.
| Shape | Type | Size |
|---|---|---|
| Acute angle | greater than 0° and less than 90° | |
| Right angle | exactly 90° | |
| Obtuse angle | greater than 90° and less than 180° | |
| Straight angle | exactly 180° | |
| Reflex angle | greater than 180° and less than 360° | |
| Full angle | exactly 360° |
How to tell which type an angle is
- Measure the angle. Measure the angle in degrees with a protractor or the online protractor.
- Compare with 90°. Less than 90° is acute; exactly 90° is a right angle.
- Compare with 180°. Between 90° and 180° is obtuse; exactly 180° is a straight angle.
- Compare with 360°. Between 180° and 360° is reflex; exactly 360° is a full angle.
Acute angle
An acute angle is greater than 0° and less than 90°. The word comes from the Latin acutus, "sharp", and acute angles do look sharp and pointy. All three angles of an equilateral triangle are acute (60° each).
Real-life examples: the tip of a pizza slice, a slice of a pie chart, the angle of a ramp, scissors half open. See the 45° angle page for more.
Right angle
A right angle is exactly 90°, a quarter of a full turn. Lines that meet at a right angle are perpendicular. In diagrams a right angle is marked with a small square instead of an arc.
Real-life examples: the corner of a book, a door frame, where a wall meets the floor, the hands of a clock at 3:00. See the 90° angle page for more.
Obtuse angle
An obtuse angle is greater than 90° and less than 180°. It is wider than a square corner but has not flattened into a line yet. Obtusus means "blunt" in Latin.
Real-life examples: an open laptop screen, a reclining chair, the corners of a hexagon (120°), the hands of a clock at 5:00 (150°). See the 120° angle page for more.
Straight angle
A straight angle is exactly 180°: its two arms point in opposite directions and form a straight line. It equals two right angles.
Real-life examples: a straight line, a flat-open book, the hands of a clock at 6:00. See the 180° angle page for more.
Reflex angle
A reflex angle is greater than 180° and less than 360°. Every pair of arms makes two angles: the smaller one and a reflex one going the long way around. They always add up to 360°.
Real-life examples: the outside corner of a building, a Pac-Man shape (the part that is not the mouth), turning more than halfway around. See the 270° angle page for more.
Full angle
A full angle (also called a complete angle, full turn or perigon) is exactly 360°: the arm rotates all the way around and lands back where it started.
Real-life examples: one complete turn of a wheel, a full spin, a clock hand going all the way around. See the 360° angle page for more.
Angle pairs
| Pair | Rule | Example |
|---|---|---|
| Complementary | Add up to 90° | 30° + 60° |
| Supplementary | Add up to 180° | 110° + 70° |
| Explementary (conjugate) | Add up to 360° | 100° + 260° |
| Adjacent | Share a vertex and one arm, no overlap | The two angles on either side of a door hinge |
| Linear pair | Adjacent and supplementary (form a straight line) | Two angles made by a line crossing another |
| Vertical (vertically opposite) | Opposite each other where two lines cross; always equal | The top and bottom angles of an X |
When a line crosses two parallel lines you also get corresponding angles (equal), alternate interior angles (equal) and co-interior / same-side interior angles (supplementary).
Measure any angle and the online protractor tells you its type automatically. Or browse all angles from 1° to 360°.
Frequently asked questions
What are the 6 types of angles?
By size: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°), reflex (between 180° and 360°) and full (exactly 360°). Some textbooks also list the zero angle (0°).
Is 90 degrees acute or obtuse?
Neither. An angle of exactly 90° is a right angle. Acute angles are strictly less than 90° and obtuse angles strictly more than 90°.
What is the difference between complementary and supplementary angles?
Complementary angles add up to 90° (like 30° and 60°). Supplementary angles add up to 180° (like 50° and 130°). A handy memory trick: C comes before S in the alphabet, and 90 comes before 180.
Can a triangle have an obtuse angle?
Yes, but only one. The three angles of a triangle add up to 180°, so if one angle is more than 90°, the other two must share less than 90°.