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:
This angle is less than 90°, but more than 0°. Examples of acute angles are 20°, 22°, 47°, 65°, 89°
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°.
This angle is more than 90°, but less than 180°. Examples of obtuse angles are 96°, 110°, 138°, 175°, 189°
A straight line is exactly 180°, and the two arms are in a straight line.
A reflex angle is more than 180°, but less than 360°. Examples of reflex angles are 190°, 232°, 285°, 315°, 359°
A revolution is a complete turn – it is exactly 360°. When turned, it turns one full circle.
In addition to these basic angles, there are some special types of angles formed when a transversal intersects two parallel lines.
The line XY forms 8 angles, and they are corresponding angles, alternate angles, and co-interior 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.
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.
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.
1. In the figure, what is x?
Since they are corresponding angles, x = 70°
Since the two angles are alternate angles, x = 120°.
x and 110° are co-interior angles, and will add up to 180°.
So x = 180° – 110°
In order to show that , 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.