Question 810552
Find the least positive angle measurement that is coterminal with -40 degrees.
<pre>
Let's draw an angle of -40°.  Negative angles rotate clockwise from the
right side of the x-axis:

{{{drawing(400,400,-1.5,1.5,-1.5,1.5, 
locate(.4,-.1,"-40°"),
red(line(-2,0,2,0),line(0,-2,0,2), arc(0,0,1.7,-1.7,320,360),
arc(0,0,.7,-.7,320,360)),

line(0,0,cos(40*pi/180),-sin(40*pi/180)) )}}}

"Coterminal" means "ends up at the same place."

Let's indicate with a green arc the smallest positive angle that
starts at the right hand side of the x-axis and rotates 
counter-clockwise and ends up at the same line that -40°
ends up at. 

The angle we need will be measured by the green counter-clockwise
arc below:

{{{drawing(400,400,-1.5,1.5,-1.5,1.5, 
locate(.4,-.1,"-40°"),
red(line(-2,0,2,0),line(0,-2,0,2), arc(0,0,1.7,-1.7,320,360),
arc(0,0,.7,-.7,320,360)),green(arc(0,0,1.5,-1.5,0,320)),

line(0,0,cos(40*pi/180),-sin(40*pi/180)) )}}}

The amount of rotation done by the -40° is 40°

So the amount of counter-clockwise rotation that will be needed
for the angle indicated by the green arc is 360°-40° or 320°.

Answer: 320°

Edwin</pre>