An angle is the region of a plane between two rays that share a common origin. The rays are called arms and the common origin is the vertex.
To measure angles, the unit degree (º) is most frequently used.
Types of Angles
An acute angle measures between 0º and 90º.
A right angle measures exactly 90º.
An obtuse angle measures between 90º and 180º.
A straight angle measures exactly 180º.
An reflex angle measures between 180º and 360º.
A negative angle measures less than 0º.
Negative angles rotate in a clockwise direction.
A negative angle can be transformed into a positive angle by adding 360º to it.
−30º = 360º − 30º = 330º
Congruent angles have the same measure.
Adjacent angles have a common side and a common vertex.
Complementary angles sum 90°.
Supplementary angles sum 180°.
Vertical Angles or Opposite Angles
The vertical angles share the common vertex and the sides of one are an extension of the sides of the other.
The angles 1 and 3 are equal.
The angles 2 and 4 are equal.
The angles 1 and 2 are equal.
Alternate Interior Angles
The angles 2 and 3 are equal.
Alternate Exterior Angles
The angles 1 and 4 are equal.
Operations with Angles
The sum of two angles is another angle whose amplitude is the sum of the amplitudes of the two initial angles.
The subtraction of two angles is another angle whose amplitude is the difference between the amplitude of the higher angle and the lower angle.
Multiplying an Angle by a Number
Multiplying a number by an angle is another angle whose amplitude is the amplitude of the angle multiplied by as many times as specified by the number.
Dividing an Angle by a Number
The division of an angle by a number is another angle that is multiplied by this number and gives the original angle.