What are Angles?
In geometry, an angle is formed when two rays are joined at their endpoints. These rays are referred to as the angle’s sides or arms.
Real World Examples of Angle
The angle can be seen on wall clocks, and are made by the clock hands. A right angle is created when the small hand is at 3 and the big hand is at 12.
Angles are all around us. Here are some examples:
Angle Components
The two main components of an angle are the arms and the vertex.
Arms of the Angles
The arms of the angle are the two rays that meet at a common point to form the angle. Analyze the diagram below; it shows that OP and OQ are the arms of angle POQ.
The Angle's Vertex
The two rays share a common endpoint called the vertex. Looking at the figure, vertex O is marked as the point where the two arms meet.
What are Degrees?
Degrees are a unit of measurement for angles. Consider breaking a circle into 360 equal pieces. A “one-degree angle” is defined as an angle that rotates through 1/360 of a circle and measures 1. It takes 360 degrees to complete a full circle.
Solved Angles & Degrees Examples
Example 1:
Find the measure of angle
Solution:
An angle that turns \(\frac{1}{360}~th\) of a circle measures 1 degree.
An angle that turns through \(\frac{95}{360}~th\) of a circle measures 95 degrees.
So, the measure of the angle is \(95^{\circ}\).
Example 2:
Find the measure of angle
Solution:
Step 1: Write \(\frac{1}{2}\) as an equivalent fraction with a denominator of 360.
\(=\frac{1\times 180}{2\times 180}=\frac{180}{360}\)
Step 2: Write \(\frac{180}{360}\) in degrees. An angle that turns through
\(\frac{180}{360}~th\) of a circle measures 180 degrees.
So, the measure of angle is \(180^{\circ}\)
Example 3:
The spinner is split into eight equal sections. What is the measurement of the angles formed by the parts?
Solution:
Step 1: Write a fraction that represents 1 part.
Because the spinner has 8 equal parts,
1 part can be represented by the fraction \(\frac{1}{8}\).
Step 2: Write \(\frac{1}{8}\) as an equivalent fraction with a denominator of 360.
\(\frac{1}{8}=\frac{1\times 45}{8\times 45}=\frac{45}{360}\)
Step 2: Write \(\frac{45}{360}\) in degrees. An angle that turns through \(\frac{45}{360}~th\) of a circle measures 45 degrees.
So, the measure of angle is \(45^{\circ}\).
In geometry, an angle is formed when two rays are joined at their endpoints. These rays are referred to as the angle’s sides or arms.
The two main components of an angle are the arms and the vertex.