Naming Angles
Lines
Let me show you different kinds of lines and how we label them.
(slide the slider to change line types and move the points around)
Line Definitions
Line: passes through two points and extends to infinity in both directions, notated 
Line segment (interval): starts at a point and ends at a point, notated 
Ray: starts at a point and extends through a second point to infinity, notated 
Angles
Now, let me show you different types of angles. Play with this applet to explore the different types of angles, what they look like and how big they are. Slide the slider and watch the angle change.
Complementary and Supplementary
Complementary angles are angles that sum to $90$90°. In the diagram on the right, $\angle DOC$∠DOC and $\angle COB$∠COB are complementary.
Supplementary angles are angles that sum to $180$180°. In the diagram on the right, $\angle COD$∠COD and $\angle DOE$∠DOE are supplementary angles.
ANGLE DEFINITIONS
Acute: an angle between 0° and 90°
Right: an angle of exactly 90°
Obtuse: an angle of between 90° and 180°
Straight: an angle of exactly 180°
Reflex: an angle of between 180° and 360°
Revolution: an angle of exactly 360°
Complementary: angles that sum to 90°
Supplementary: angles that sum to 180°
Naming angles
Angles inside shapes
This quadrilateral has 4 vertices. They are labelled $A$A, $B$B, $C$C and $D$D.
The edges of the shape would be labelled like line segments.
We can call them AB, BC, CD, DA .
The angle marked has vertex (the pointy bit of the angle) at $B$B.
We label an angle by moving from one point on the line segment, through the VERTEX to a point on the the other line segment. Thus the shaded angle is called $\angle ABC$∠ABC or $\angle CBA$∠CBA. See the angle symbol at the front? This is important; it tells us that the three point names that follow make up the angle which we are talking about.
Can you see where $\angle ADC$∠ADC is ? What about $\angle DCB$∠DCB ?
Angles in lines
Lines, Line Segments (intervals) and Rays that cross create angles.
Have a play with this applet, you can create lines, line segments and rays that cross each other. Change the slider to change the type of lines, move the points to place you like, then slide the slider to show the angles that are created.
We label an angle by moving from one point on the line (line, segment or ray), through the VERTEX to a point on the the other line (line, segment or ray).
Worked Examples
Question 1
In the following, state the vertex and name the angle.
Question 2
Is this angle ACUTE, OBTUSE or REFLEX?
Question 3
In the diagram, $\angle ABD=53^\circ$∠ABD=53°, $\angle ABE=112^\circ$∠ABE=112° and $\angle DBC=131^\circ$∠DBC=131°
a) Find the measure of $\angle EBD$∠EBD
b) Deduce the measure of $\angle EBC$∠EBC