An angle can be considered positive or negative depending on the direction in which it rotates. When measuring angles, we typically use a reference point called the initial side and a reference direction called the positive x-axis.

If an angle rotates in a counterclockwise or anticlockwise direction, it is considered positive. This means that as the angle increases, it moves in the direction of the positive x-axis. For example, if we start at the positive x-axis and rotate 45 degrees counterclockwise, the resulting angle would be positive 45 degrees.

On the other hand, if an angle rotates in a clockwise direction, it is considered negative. This means that as the angle increases, it moves in the opposite direction of the positive x-axis. For instance, if we start at the positive x-axis and rotate 30 degrees clockwise, the resulting angle would be negative 30 degrees.

To understand this concept further, let’s consider some real-life examples. Imagine you are standing at a crossroad, facing north. If you turn to your left and face west, you have rotated in a counterclockwise direction, and the angle you have formed is positive. Conversely, if you turn to your right and face east, you have rotated in a clockwise direction, and the angle you have formed is negative.

In mathematics, we can represent angles using different units of measurement. The most common units are degrees and radians. In the degree method, a full rotation is 360 degrees, with positive angles measured counterclockwise and negative angles measured clockwise.

In the radian method, a full rotation is equal to 2π radians, where π is approximately 3.14159. Similar to degrees, positive angles in radians are measured counterclockwise, and negative angles are measured clockwise.

It’s important to note that angles can also be measured beyond a full rotation. These angles are called coterminal angles. Coterminal angles share the same initial and terminal sides but differ in the number of complete rotations they make. For example, an angle of 390 degrees and an angle of 30 degrees are both coterminal angles because they end at the same position.

To summarize, an angle is considered positive when it rotates counterclockwise from the initial side, and it is negative when it rotates clockwise. The choice of units (degrees or radians) determines the specific numerical value assigned to the angle. Understanding the concept of positive and negative angles is crucial in various fields, including geometry, physics, and engineering.