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Classification of Angles

Angles can be classified according to their degree measures.

i.e, classification of angles on the basis of their degree measures are given below:

Acute Angle:

An angle whose measure is more than 0° but less than 90° is called an acute angle.

Definition of Acute Angle:

An angle measuring less than 90" is called an acute angle.

Angles having magnitudes 30°, 40°, 60° are all acute angles.

In the adjoining figure, ∠XOY represents an acute angle.

∠XOY < 90°

$Acute Angle$

In the right side figure, ∠AOB is an acute angle.

$Acute Angle$

Examples of Acute Angle:

(i) Angles between two adjacent edges of scissors, etc.

(ii) Sun-rays make acute angle with the ground in the morning.

Right Angle:

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

Definition of Right Angle:

An angle measuring 90° is called a right angle.

In the adjoining figure, ∠ABC represents a right angle.

∠ABC = 90°

$Right Angle$

The arms of a right angle are perpendicular to each other.

In figure below, ∠AOB is a right angle.

$Right Angle$

Examples of Right Angle:

Corner of a room and Pillar on a ground form right angles.

Obtuse Angle:

An angle whose measure is more than 90° but less than 180° is called an obtuse angle.

Definition of Obtuse Angle:

An angle greater than a right angle but less than two right angles is called an obtuse angle.

Its measure is more than 90° but less than 180°.

In the adjoining figure, ∠XYZ represents an obtuse angle.

∠XYZ > 90°

∠XYZ < 180°

$Obtuse Angle$

In figure, ∠ABC is an obtuse angle.

$Obtuse Angle$

Examples of Right Angle:

Two adjacent sides of a microphone set, two edges of a book reading desk and two edges of the roof of a house form obtuse angles.

Straight Angle:

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

Definition of Straight Angle:

An angle whose measure is 180° is called a straight angle.

In the adjoining figure, ∠XOY represents a straight angle.

∠XOY = 180°

$Straight Angle$

In figure, ∠ABC is a straight angle extend in opposite directions.

$Straight Angle$

Examples of Straight Angle:

Tubelight, pencil, a line segment form straight angles.

Reflex Angle:

A reflex angle is an angle which is larger than a straight angle. Its measure is more than 180º, but less than 360°.

Definition of Reflex Angle:

An angle whose measure is more than 180° but less than 360° is called a reflex angle.

In the adjoining figure, ∠POQ is a reflex angle.

∠POQ > 180°

∠POQ < 360°

$Reflex Angle$

In figure, ∠CBA is a reflex angle.

$Reflex Angle$

Angles having magnitudes 220°, 250°, 310° are all reflex angles.

Complete Angle:

A complete angle is formed when the revolving ray OP (say) has made one complete revolution around the fixed point O after starting from the fixed initial position OA. The measure of a complete angle is 360°.

Definition of Complete Angle:

An angle whose measure is equal to 360° is called a complete angle.

$Complete Angle$

In the adjoining figure, ∠BOA represents a complete angle.

$Complete Angle$

Examples of Complete Angle:

If the minute hand of a clock starts from point A (say) and returns back to this point after one complete revolution, then a complete angle of 360° is formed.