Problem 101 - Algebra and Trigonometry

Question

What is an angle?

Step-by-Step Solution

Answer

An angle is a shape, created by two lines diverging from a common point. The lines are known as sides and the common point as the vertex. Angles are represented by Greek or Roman letters and are classified into various types based on their measures.

Step 1: Definition

An angle is a figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Step 2: Representation

Angles are usually designated by Greek letters (\( \alpha \), \( \beta \), \( \gamma \), etc.) or by Roman letters (A, B, C, etc.). An angle can also be represented by three points with the middle point being the vertex.

Step 3: Types of Angles

There are several different types of angles based on their measure. They are classified as acute angle (less than 90 degrees), right angle (exactly 90 degrees), obtuse angle (greater than 90 but less than 180 degrees), straight angle (exactly 180 degrees), reflex angle (greater than 180 but less than 360 degrees), and full rotation (exactly 360 degrees).