Angles

Angles are a fundamental concept in geometry. They are formed when two rays meet at a single point, called the vertex.

An angle is the measure of rotation between two rays that share a common endpoint, called the vertex.

A full turn, or complete circle, is divided into 360 equal parts called degrees, a convention established by ancient Babylonian astronomers.

A degree is a unit of angle measurement. A full turn measures \(360^\circ\).

The measure of an angle in degrees is the fraction of a full turn it represents.

Calculate the measure of an angle that represents one-third of a full turn.

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 \(180^\circ\).

1. Place the protractor’s origin (center point) over the vertex of the angle.
2. Align one ray of the angle with the protractor’s baseline (the \(0^\circ\) mark).
3. Observe where the other ray intersects the protractor’s scale.
4. Read the angle measure in degrees from the scale.

Measure the following angle.

1. Draw a ray starting from a point (the vertex).
2. Place the protractor’s origin over the vertex and align the baseline with the ray.
3. Locate the desired angle measure on the protractor’s scale and mark the point.
4. Draw a second ray from the vertex through the marked point to form the angle.

In geometry, angles are classified based on their measure. The following table defines four main types of angles: straight, right, acute, and obtuse.

Name	Fraction of a Circle	Angle Measure	Figure
Acute Angle	Less than \(\dfrac{1}{4}\)	Less than \(90^{\circ}\)
Right Angle	\(\dfrac{1}{4}\)	\(\dfrac{1}{4} \text{ of } 360^{\circ} = 90^{\circ}\)
Obtuse Angle	Between \(\dfrac{1}{4}\) and \(\dfrac{1}{2}\)	Between \(90^{\circ}\) and \(180^{\circ}\)
Straight Angle	\(\dfrac{1}{2}\)	\(\dfrac{1}{2} \text{ of } 360^{\circ} = 180^{\circ}\)