



When we
have angles in circles,



sometimes
we draw in the lines ... 











But
sometimes we don't. 


WHAT? AN
ANGLE WITH NO LINES? 


JUST HOW
ARE YOU GOING TO DO THAT??? 





Easy,
like this: 


1) Draw a
circle. 


2) Put a
point in the center. 


3) Put a
point where each line would touch the circle 


if we did draw the lines. 


4) Label
the points with letters. 











Now we
can say angle BAC. 


Let your
mind put in the lines. 











Maybe you
can see that Angle BAC 


is not
the same as Angle BCA 











Now we
can put together some stuff 


from the
last couple of pages ... 





Example: 











Angle BEC
is 100 degrees. 


What is
the measure of angle DAC? 





Let's
draw in some lines ... 











1) Since
angle BEC is 100 degrees, 


angle AED
is also 100 degrees. 











2) All of
the angles in the circle add up to 360 degrees. 


Angle AEB
and angle DEC are the same as each other. 





AEB
+ 100 + DEC + 100 = 360



AEB + DEC = 160 


AEB =
80 DEC =
80 











3) Now we
can think about angle DAC. 


Get rid
of a few lines and draw a few others ... 











A couple
of pages ago we talked about stuff like this. 


Angle DAC
and angle DEC end up at the same points. 


Angle DEC
starts at the center. 


Angle DAC
starts at the edge. 


Angle DEC
is 80 degrees 


so angle
DAC is 40 degrees. 











copyright 2005 Bruce Kirkpatrick 
