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Types of angles

There are six different types of angles – acute, right, obtuse, straight, reflect and revolution angles. Each of these angles is formed by the sizes made by two rays. The angles are classified according to their sizes. Let’s look at these six different types of angles:

 

Acute angle

This angle is less than 90°, but more than 0°. Examples of acute angles are 20°, 22°, 47°, 65°, 89°

types of angles-acute angle

Right angle

An angle that forms a sharp corner like that of a corner of a whiteboard, is called a right angle. A right angle is exactly 90°.

right angle

 

Obtuse angle

This angle is more than 90°, but less than 180°. Examples of obtuse angles are 96°, 110°, 138°, 175°, 189°

obtuse angle

 

Straight line

A straight line is exactly 180°, and the two arms are in a straight line.

types of angles-straight line

Reflex angle

A reflex angle is more than 180°, but less than 360°. Examples of reflex angles are 190°, 232°, 285°, 315°, 359°

types of angles-reflex angle

Revolution

A revolution is a complete turn – it is exactly 360°. When turned, it turns one full circle.

types of angles-revolution

 

In addition to these basic angles, there are some special types of angles formed when a transversal intersects two parallel lines.

transversal

The line XY forms 8 angles, and they are corresponding angles, alternate angles, and co-interior angles.

types of angles-parallel line angles

 

Corresponding angles

They are on the same side of the transversal, and in the same position on both the parallel lines. They are equal in size, and form a ‘F’ shape on the parallel lines.

types of angles-corresponding angles

Alternate angles

These angles are on opposite sides of the transversal, and lie in between the parallel lines. They are equal in size and form a ‘Z’ shape.

types of angles-alternate angles

Co-interior angles

They are on the same side of the transversal, and between the parallel lines. These angles will add up to 180° and form a ‘C’ shape.

types of angles-co interior angles

 

Examples

1. In the figure, what is x?

corresponding angle of 70°

Since they are corresponding angles, x = 70°

2.

alternate angle of 120°

Since the two angles are alternate angles, x = 120°.

 

3.

co-interior angle of 110°

x and 110° are co-interior angles, and will add up to 180°.

So x = 180° – 110°

= 70°

4.

alternate angle of 70°

In order to show that  AB~vert~CD , we need to prove that the alternate angles are equal to each other. Here they are both 70°, so AB and CD are parallel lines.