Subjects
Grades
Angles
Concept sheet | Mathematics
Secondary
1-2
An angle is formed by two lines that meet or intersect.
Each of the lines (or rays) in the angle is called the side of the angle and the point at which they meet is called the vertex.
In the image below, |A| is the vertex of the angle. The line segments |AB| and |AC| form the sides of angle |A.|
There are three ways to name an angle. It can be named by its vertex, by a number inscribed in the angle opening, or by three points. When naming an angle by three points, the middle letter always designates the vertex of the angle.
Consider the angle below.
The angle can be named in three different ways:
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by its vertex: |\angle A|;
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by a number: |\angle 1|;
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by three points: |\angle BAC| or |\angle CAB.|
An angle is usually measured in degrees (°) using a protractor.
One degree corresponds to one three hundred and sixtieth |\left(\dfrac{1}{360}\right)| of the circumference of a circle.
The symbol "|\mathrm{m}\angle|" means measurement of angles. It is also possible to measure an angle in radians.
In a circle, a radian is the measure of a central angle which intercepts at an arc length that is equal to the radius of the circle.
To convert degrees to radians, and vice versa, use the following proportion.
||\dfrac{n^{\circ}}{360^{\circ}}=\dfrac{\theta \text{rad}}{2\pi \text{rad}}||
where |\pi \approx 3.1415...| and |\theta| is a real number.
Read the following concept sheet to learn more about measuring angles in radians and the conversion of degrees into radians:
Trigonometric Angles (Radians).