Geometry › Angles

Angles

An angle measures how much something has turned. Drag below and watch the size change in degrees.

Angle explorer

Click anywhere to point the second arm

try pointing past 180°

Angle

60°

Acute angle

Acute: less than 90°
Right: exactly 90°
Obtuse: between 90° and 180°
Reflex: more than 180°

What is an angle?

Two lines that share an end-point form an angle. The size of the angle is the amount of rotation from one line to the other — measured in degrees. A full turn is 360°.

The names

Acute — less than 90°. Sharp.
Right — exactly 90°. The corner of a square.
Obtuse — between 90° and 180°. Open.
Straight — exactly 180°. A flat line.
Reflex — between 180° and 360°.
Full — 360°. Back where you started.

Why 360?

The number 360 is divisible by lots of things — 2, 3, 4, 5, 6, 8, 9, 10, 12 — so common fractions of a turn come out as whole numbers of degrees. That's why the ancient Babylonians chose it.

Special pairs

Two angles are complementary if they add to 90°.
Two angles are supplementary if they add to 180°.
Vertically opposite angles (across an X) are equal.

Triangles and quadrilaterals

Triangle: angles sum to 180°.
Quadrilateral: angles sum to 360°.
n-gon: (n − 2) × 180°.