Angles and it's Types
Types of Angles Based on Measurement
The space formed when two rays meet each other at a common point is called an angle. Angles can be classified both on their measurement and the way they are rotated. Based on the measurement, angles are classified as follows. Observe the following figure to relate to the different kinds of angles explained below.
Acute Angle
Any angle that is less than 90° is an acute angle. If two rays intersect at a vertex, forming an angle that is less than 90°, an acute angle is formed. Some examples of acute angle are 20°,30°,45°,60°. Observe the figure which shows that ∠XYZ is an acute angle.
Right Angle
If the angle formed between two rays is exactly 90° then it is called a right angle or a 90° angle. Observe the figure which shows that ∠AOB s a right angle or a 90° angle.
Obtuse Angle
Any angle that is greater than 90° but less than 180° is an obtuse angle. The angle formed by the rays PQ and QR in the figure is an obtuse angle. Some examples of obtuse angles are 110°, 130°, 145°,165°.
Straight Angle
As the name suggests, a straight angle is a straight line, and the angle formed between two rays is exactly equal to 180°. At a straight angle, the two rays are opposite to each other. A straight angle can be formed by combining two adjacent right angles or in other words two right angles make up a straight angle. In the figure, ∠SRT is a 180° angle or a straight angle.
Reflex Angle
An angle that is greater than 180° and less than 360° is called a reflex angle. In the figure, ∠ABC is a reflex angle. Examples of reflex angles are 210°, 250°, 310°.
Full Rotation Angle
A full rotation angle is formed when one of the arms of the angle goes on a complete rotation or makes a 360°. In the figure, ∠MNR = 360° and is termed as a full rotation angle.
Types of Angles Based on Rotation
The next type of angles is based on the direction of rotation of one arm of an angle. When two lines intersect and meet at a point, an angle is formed. Let us discuss the angle types on the basis of rotation.
Positive Angles
Positive angles are the ones in which angles are rotated from the base in the counter-clockwise or anti-clockwise direction. In the figure shown below, when side 1(AB) is rotated in the anti-clockwise direction by an angle θ, a positive angle is formed.
Negative Angles
Negative angles are the ones in which angles are rotated from the base in the clockwise direction. In the figure shown below, when side 1 (DE) is rotated in the clockwise direction by an angle θ, a negative angle is formed.
Types of Angle Pairs
A pair of angles denotes two angles. Let us read about the various angle pairs in geometry.
Adjacent Angles
For two angles to be adjacent angle, the following conditions should be true.
- Two angles share a common vertex.
- Two angles share a common arm.
- There are two arms that are not common.
Complementary Angles
When the sum of two angles is equal to 90°, they are called complementary angles. The two angles can be of any measure such that they sum up to 90°. For example, the two angles can be 30° and 60°. Here, one angle is the complement of the other angle.
Supplementary Angles
When the sum of two angles is equal to 180°, they are called supplementary angles. The two angles when added make up 180°. For example, 110° and 70° make up 180°. So these two angles are said to be supplementary. Here, one angle is the supplement of another angle. For example, the supplement of 60° is (180° - 60°), which is 120°.
Alternate Interior Angles
When a line or a transversal passes through two parallel lines the angles formed at the opposite sides of the line or the transversal are called alternate interior angles which are equal.
Alternate Exterior Angles
When a line or a transversal passes through two parallel lines the angles that are formed at the external side of the line or transversal are called alternate exteriir angles which are equal.
Corresponding Angles
When a line or a transversal passes through two parallel lines the angles that are formed at the same position or on the same side of the transversal are corresponding angles and these angles are congruent.
Vertical Angles
When two lines intersect each other, the angles opposite to each other are equal and are termed as vertical angles, or, vertically opposite angles.
Observe the following figure to relate to the angles given above.
