Definition of a Figure Formed by Two Straight Lines

A figure formed by two straight lines having a common point is called an angle. In geometry, an angle is a fundamental concept that helps us understand the relationship between two intersecting lines or line segments.

Explanation and Properties of an Angle

An angle is formed when two straight lines originate from a common point, known as the vertex. The two lines are referred to as the sides of the angle. The sides can be named by using the vertex as a reference point, such as "side AB" and "side AC" if the vertex is denoted as point A.

Notation: Angles are commonly represented using a curved line between the sides or by a small arc drawn in the interior of the angle. For instance, angle ABC can be denoted as ∠ABC or ∠B.

Types of Angles: Angles can be classified based on their measures. Here are some common types:

1. Acute Angle: An angle less than 90 degrees is called an acute angle.
2. Right Angle: An angle measuring exactly 90 degrees is called a right angle.
3. Obtuse Angle: An angle greater than 90 degrees but less than 180 degrees is called an obtuse angle.
4. Straight Angle: An angle measuring exactly 180 degrees is called a straight angle.
5. Reflex Angle: An angle greater than 180 degrees but less than 360 degrees is called a reflex angle.

Properties of Angles: Angles possess several important properties, some of which include:

1. Angle Sum Property: The sum of the measures of the angles around a point is always 360 degrees. For example, if we have three angles formed around a point, their measures will add up to 360 degrees.
2. Angle Bisector: An angle bisector is a line or ray that divides an angle into two congruent (equal) parts. The bisector passes through the vertex of the angle.
3. Vertical Angles: When two lines intersect, they form two pairs of vertical angles. Vertical angles are always congruent, meaning they have equal measures.

Importance of Angles:

Angles are vital in various fields, including mathematics, physics, engineering, and architecture. They help us understand the relationships between lines, shapes, and objects, enabling us to solve problems, measure distances, and create accurate designs. Additionally, angles play a crucial role in trigonometry, which deals with the study of triangles and their properties.

In conclusion, a figure formed by two straight lines having a common point is called an angle. Understanding angles and their properties is essential for various applications in geometry and other disciplines.