Angles
Angles are a fundamental concept in geometry. They are formed when two rays meet at a single point, called the vertex.
Definition
Definition Angle
An angle is the measure of rotation between two rays that share a common endpoint, called the vertex.
Degrees
A full turn, or complete circle, is divided into 360 equal parts called degrees, a convention established by ancient Babylonian astronomers.
Definition Degree Unit
A degree is a unit of angle measurement. A full turn measures \(360^\circ\).
Definition Measure of an Angle in Degrees
The measure of an angle in degrees is the fraction of a full turn it represents.
Example
Calculate the measure of an angle that represents one-third of a full turn.
$$\begin{aligned}\text{Angle} &= \frac{1}{3} \text{ of } 360^\circ \\&= 360^\circ \div 3 \\&= 120^\circ\end{aligned}$$
Measuring and Drawing Angles with a Protractor
Definition Protractor
A protractor is a tool used to measure and draw angles in degrees. It is typically a semi-circular tool with a scale marked from \(0^\circ\) to \(180^\circ\).
Method Measuring an Angle with a Protractor
- Place the protractor’s origin (center point) over the vertex of the angle.
- Align one ray of the angle with the protractor’s baseline (the \(0^\circ\) mark).
- Observe where the other ray intersects the protractor’s scale.
- Read the angle measure in degrees from the scale.
Example
Measure the following angle.
The angle measures \(140^\circ\).
Method Drawing an Angle with a Protractor
- Draw a ray starting from a point (the vertex).
- Place the protractor’s origin over the vertex and align the baseline with the ray.
- Locate the desired angle measure on the protractor’s scale and mark the point.
- Draw a second ray from the vertex through the marked point to form the angle.
