Angles

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.

Angle


To measure angles, the unit degree (º) is most frequently used.

Types of Angles

Acute Angle

Acute Angle An acute angle measures between and 90º.

Right Angle

Right AngleA right angle measures exactly 90º.

Obtuse Angle

Obtuse AngleAn obtuse angle measures between 90º and 180º.

Straight Angle

Straight Angle A straight angle measures exactly 180º.

Reflex Angle

Reflex Angle An reflex angle measures between 180º and 360º.

Negative Angle

Negative Angle 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

Congruent AnglesCongruent angles have the same measure.

Adjacent Angles

Adjacent Angles

Adjacent angles have a common side and a common vertex.

Complementary Angles

Complementary Angles

Complementary angles sum 90°.

Supplementary Angles

Supplementary Angles

Supplementary angles sum 180°.


Vertical Angles or Opposite Angles

Vertical 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.

Corresponding Angles

Corresponding Angles

 

The angles 1 and 2 are equal.

Alternate Interior Angles

Alternate Interior Angles

 

The angles 2 and 3 are equal.

Alternate Exterior Angles

Alternate Exterior Angles

 

The angles 1 and 4 are equal.

Operations with Angles

Adding Angles

The sum of two angles is another angle whose amplitude is the sum of the amplitudes of the two initial angles.

Adding Angles

Subtracting 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.

Subtracting Angles

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.

Multiplying an Angle by a 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.

Dividing an Angle by a Number I:4 =Dividing an Angle by a Number II