2.3 Different Angles
Mathematicians use different names for different angles. This makes it easier when communicating so that we all talk about the same thing. 
Acute Angle 
Right Angle 
Obtuse Angle 
Straight Angle 




Λ < 90º

Λ = 90º

90º < Λ < 180º

Λ = 180º


Always 90 degrees. 
Larger than 90 and less than 180 degrees. 
Always 180 degrees. 


Bisector 

A bisector is not an angle but a ray that come from the vertex which divides an angle into two equally large angles. 


Top Angles and Base Angles 

In an isosceles triangle, two sides are equally long. There is a top angle and two base angles. The base angles are equal. 


Side Angles 

The angles v_{1} and v_{2} are example of supplementary angles. Supplementary angles are together 180º. They have one common ray and the other ray creates a straight line. 


Vertical Angles 

If two lines intersect each other, four angles are created. The angles v_{1} and v_{2 }are examples of vertical angles. Vertical angles are equal. 



Angles Between Parallel Lines
If a line (transversal) intersects two parallel lines, eight angles are created. In the pictures below, all the angles are not marked, but it is important to understand that there are in fact 8 angles. 
Corresponding Angles 

The lines l_{1} and l_{2} are parallel and are intersected by a third line (transversal). v_{1} and v_{2 }are corresponding angles. Corresponding angles are equal. 

There are 3 more corresponding angle pairs which have not been marked in the figure. 
Alternate angles in Parallel Lines 

The lines l_{1} and l_{2} are parallel and are intersected by a third line (transversal). v_{1} and v_{2} as well as v_{3} and v_{4} are alternate angles. Alternate angles of parallel lines are equal to each other.
Λv_{1} = Λv_{2} and Λv_{3} = Λv_{4}. 

There are an additional two pairs of alternate angles which we have not marked. 
Supplementary Angles 

The lines l_{1} andi l_{2}are parallel. Angles which together have a sum of 180° are called supplementary angles. Adjacent angles are an example of supplementary angles.
The angles Λv_{1} + Λv_{2} = 180º. 

There are an additional three supplementary angle pairs which we have not marked. 

Complementary Angles 

Complementary angles are angles which together create a sum of 90°. Λv_{1} + Λv_{2} = 90°. 
