Reference

Types of Angles

Concept

Angle

An angle is formed by two rays that share a common endpoint. The common endpoint is the vertex, and the rays are the sides of the angle.

The sides of this angle are BA and BC and its vertex is B. The region between the sides is the interior of the angle, while the region outside is its exterior. There are different ways to name an angle. Each name begins with the symbol ∠.

Naming Method	Explanation	Example
Using the vertex	Use the vertex letter when only one angle is located at that vertex.	∠ B
Using three points	Use one point on each side and the vertex. The vertex must appear in the middle.	∠ABC or ∠CBA
Using a number or a Greek letter	Use the number or letter written inside the angle.	∠ 1 or ∠ α

Concept

Acute Angle

An acute angle is an angle whose measure is greater than 0^(∘) but less than 90^(∘).

Applet showing when an angle is acute and when it is not.

When using radians as the unit of measure, an angle is acute when its measure is greater than 0 but less than π2, or about 1.57, radians.

Concept

Right Angle

A right angle is an angle whose measure is exactly 90^(∘). In diagrams, right angles are denoted with a square angle marker.

When using radians as the unit of measure, an angle is a right angle when its measure is exactly π2, or about 1.57, radians.

Concept

Obtuse Angle

An obtuse angle is an angle whose measure is greater than 90^(∘) but less than 180^(∘).

When using radians as the unit of measure, an angle is obtuse when its measure is greater than π2, or about 1.57, but less than π, or about 3.14, radians.

Concept

Straight Angle

A straight angle is an angle whose measure is exactly 180^(∘).

When using radians as the unit of measure, an angle is a straight angle when its measure is equal to π, or about 3.14, radians.

Concept

Reflexive Angle

A reflexive angle is an angle whose measure is greater than 180^(∘) but less than 360^(∘). An alternative name for this type of angle is reflex angle.

When using radians as the unit of measure, an angle is a reflexive angle when its measure is greater than π, or about 3.14, but less than 2π, or about 6.28, radians.

Concept

Complete Angle

A complete angle is an angle whose measure is exactly 360^(∘). Alternative names for this type of angle are full angle, round angle, and perigon.

When using radians as the unit of measure, an angle is a complete angle when its measure is equal to 2π, or about 6.28, radians.

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