Types of Angles
When two rays or lines meet at a common point, an angle is formed and each angle differs in its measure. There are various types of angles in geometry, like, acute angle, obtuse angle, right angle, reflex angle, and straight angle. For example, an acute angle is an angle that is less than 90° and an obtuse angle is one that is greater than 90°. There are some special types of angle pairs too. Let us learn about the different types of angles in detail.
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 angles, 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 exterior 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.
Topics Related to Types of Angles
Check out some interesting articles related to angles.
Solved Examples on Types of Angles
-
Example 2: Find the measures of angles 'x', 'y', and 'a' in the figure.
Solution:
From the figure, we note that a transversal line intersecting two parallel lines forming the alternate interior and exterior angles. Two pairs of alternate interior angles that are formed by a transversal are congruent to each other. Therefore, ∠x = 75° and ∠y = 105°.
It can be seen that angle 'x' is vertically opposite to angle 'a' and they are congruent. Therefore, ∠a = ∠x = 75°.
FAQs on Types of Angles
How are the Types of Angles Classified?
An angle is formed when two rays or lines intersect at a point. The types of angles are classified based on various factors like their measurements or the way they are rotated. Considering these facts, the types of angles based on measurements are acute angle, obtuse angle, right angle, straight angle, full rotation angle, reflex angle. Based on rotation, the types of angles are classified as positive and negative angles.
What are the Types of Angle Pairs?
The types of angle pairs are as follows.
- Adjacent angles: They share a common vertex and one common arm. The other two arms are non-overlapping.
- Complementary angles: When the sum of two angles is 90°, the angles are called complementary angles. Each angle is called the complement of the other angle.
- Supplementary angles: Two angles are considered supplementary when they sum up to 180°. Each angle is called the supplement of the other angle.
- Alternate interior angles: The angles formed when a transversal passes through two parallel lines at the interior sides of the transversal are called alternate interior angles and they are congruent.
- Alternate exterior angles: The angles formed when a transversal passes through two parallel lines at the exterior sides of the transversal are called alternate exterior angles and they are congruent.
- Corresponding angles: The angles formed on the same side when a transversal passes through two parallel lines are called corresponding angles which are equal.
- Vertical angles: The angles formed when two lines intersect are vertical angles. The opposite angles formed by this intersection are equal in measure and are also known as vertically opposite angles.
What are the Types of Angles that Measure Less than 180°?
Acute and obtuse angles are the types of angles that measure less than 180°. Acute angles are always less than 90° while obtuse angles are more than 90° but always less than 180°. Examples of an acute angle are 60°, 70° and examples of obtuse angles are 110°, 125°.
What are the Types of Angles Formed When a Transversal Passes Through Two Parallel Lines?
When a transversal passes through two parallel lines, many pairs of angles are formed, such as alternate interior angles, alternate exterior angles, and corresponding angles. All these pairs of angles are equal in measure.
What is the Type of Angle that Measures More Than 180° but Less than 360°?
A reflex angle is an angle that measures more than180° but less than 360°. For example, an angle of measure 270° is a reflex angle.
What are the Types of Angles that Add Up to 90° and 180° Called?
When two angles add up to 90°, they are called complementary angles. The two angles can be of any measure such that they sum up to 90°. For example, 20° and 70° are complementary angles because they add up to 90°. When the sum of two angles is equal to 180°, they are called supplementary angles. The two angles always add up to 180°. For example, 105° and 75° are supplementary because they add up to 180°.