Recall that a line is said to be TANGENT to a circle if and only if it intersects the circle at exactly one point.
In the applet below, 2 tangent rays are drawn to a circle.
These tangents have the same endpoint located outside the circle.
You can move the BIG PURPLE POINT around to change the measure of this angle formed by these 2 tangent rays.
Note that these two tangent rays intercept two arcs of the circle: a red arc and a green arc.
You can also move the vertices of the two inscribed angles as well. The red inscribed angle intercepts the same red arc that the tangent rays intercept. The green inscribed angle intercepts the same green arc the the tangent rays intercept.
Mess around with the applet below for a few minutes and then answer the questions that follow.

Questions:
Suppose the red arc measures 300 degrees.
1) What would the measure of the green arc be?
2) What would the measure of the purple angle be?
Now suppose the green arc measures 90 degrees.
1) What would the measure of the red arc be?
2) What would the measure of the purple angle be?
Explain how you can find the measure of an angle formed by two tangents drawn to a circle from a point outside the circle.
Be sure to use the term(s) "intercepted arc(s)" at least once in your description. Be specific!