Angles are a mathematical concept used to measure the number of turns between two lines or line segments that meet at a common point. They are typically measured in degrees or radians and are often represented by the symbol "θ."
There are 6 types of angles based on measurement:
1. Acute Angle
When the two rays make any inclination between zero and ninety degrees, it is called an acute angle, i.e., 0° < angle < 90°.
The corners of an acute-angle triangle, the tip of a pencil, or the point of a star are some examples of acute angles.
2. Right Angle
When the two rays make any inclination of exactly ninety degrees, it is called a right angle, i.e., angle = 90°.
You can find it in many everyday objects, like the corners of a book or the edge of a door frame.
3. Obtuse Angle
When the two rays make any inclination of exactly ninety degrees, it is called an obtuse angle, i.e., 90° < angle < 180°.
The largest angle of the obtuse angle tangle is a key example of the obtuse angles.
Straight Angle
When the two rays make any inclination of exactly 180 degrees, it is called a straight angle, i.e., angle = 180°.
A straight angle is used with a straight edge, which is used to align something parallel to the horizontal.
Reflexive Angle
When the two rays make any inclination greater than 180 degrees but less than 270 degrees. It is called a reflex angle, i.e., 180° < Angle < 270°.
The exterior angle of any basic regular polygon is a reflex angle.
Complete Angle
When the two rays make any inclination of 360°, i.e., they overlap each other. It is called a complete angle, i.e., Angle = 360°. Here, the angle given below is a complete angle.
Based on Rotation
On the basis of measurement of rotation, an angle can be two types:
1. Positive Angles
Angles that are measured in a counterclockwise direction from the base are called positive angles. Generally, positive angles are used to represent angles in geometry. From the origin, if an angle is drawn in the first quadrant, it forms a positive angle.
2. Negative Angles
Angles that are measured in a clockwise direction from the base are called negative angles. From the origin, if an angle is drawn in the third quadrant, it forms a negative angle.
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Solved Examples on Types of Angles
Example 1: An Angle A measures 135° in measure. Which type of category does Angle A fall into?
Angle A lies between 90° to 180° in measure. Angle A is, therefore, an Obtuse Angle.
Example 2: Angle S measures 35°. Which type of category does Angle S fall into?
Angle S lies between 0° to 90° in measure. Angle S is therefore an Acute Angle.
Example 3: An angle X measures 235 degrees in measure. Which type of category does Angle X fall into?
Angle X lies between 180° to 360° in measure. Angle X is therefore a Reflex Angle.
Example 4: An angle Z measures 335°. Which type of category does Angle Z fall into?
Angle Z lies between 180° to 360° in measure. Angle Z is therefore a Reflex Angle.
Example 5: Find the complement of 40° and the supplement of 25°.
Those angles that sum up to 90°are called as Complementary angles .
The complement of 40° is 50° because (90° - 40° = 50°).
Those angles that sum up to 180°are called as Supplementary angles.
The supplement of 25° is 155° because (180° - 25° = 155°).
Practice Problems on Types of Angles
1. Identify the type of angle that measures exactly 90 degrees.
Options: A) Acute B) Right C) Obtuse D) Reflex
2. Which type of angle measures more than 180 degrees but less than 360 degrees?
Options: A) Acute B) Right C) Reflex D) Straight
3. If an angle measures 35 degrees, what type of angle is it?
Options: A) Acute B) Right C) Obtuse D) Reflex
4. Which angle is formed by the hands of a clock at 6:00?
Options: A) Acute B) Right C) Obtuse D) Straight
5. A skateboard ramp forms an angle of 175 degrees where it meets the ground. What type of angle is this?
Options: A) Acute B) Right C) Obtuse D) Reflex