👉 Angle

When two rays originate from the same endpoint and move in different directions, an angle is formed.
The angle formed by two rays lies on the same plane.
In a geometric figure, an angle is represented by three points, such as ∠BOC or ∠O.

Angle

∠BOC or ∠O

🔹 Types of Angles

Based on their measure, angles are divided into five types:

Angle

Acute Angle

Right Angle

Obtuse Angle

Straight Angle

Reflex Angle

Acute Angle

0° < θ < 90°

An angle smaller than 90° is called an acute angle.

Right Angle

θ = 90°

An angle equal to 90° is called a right angle.

Obtuse Angle

90° < θ < 180°

An angle greater than 90° but smaller than 180° is called an obtuse angle.

Straight Angle

θ = 180°

An angle equal to 180° is called a straight angle.

Reflex Angle

180° < θ < 360°

An angle greater than 180° but smaller than 360° is called a reflex angle.

🔹 Relation Between Angles

Based on the relationship between two angles, they can be divided into four types:

Angle

Adjacent Angles

Complementary Angles

Supplementary Angles

Vertically Opposite Angles

Adjacent Angles

Adjacent Angles

∠AOC is adjacent to ∠BOC.

If two angles have a common arm and a common vertex, they are called adjacent angles.

Here, OC is the common arm and O is the vertex.

Complementary Angles

Complementary Angles

∠AOC + ∠BOC = 90°

If the sum of two adjacent angles is 90°, they are called complementary angles.

Here, ∠AOC and ∠BOC are complementary to each other.

Supplementary Angles

Supplementary Angles

∠AOC + ∠BOC = 180°

If the sum of two adjacent angles is 180°, they are called supplementary angles.

Here, ∠AOC and ∠BOC are supplementary to each other.

Vertically Opposite Angles

Vertically Opposite Angles

∠AOC = opposite ∠BOD

∠AOD = opposite ∠COB

Further Learning

In the next chapters, we will study other types of angles such as Alternate Angles, Corresponding Angles, Internal Angles, and External Angles.