Copy of Angle Formed by 2 Secants (V2): What Do You See?
Recall that a SECANT is a line that crosses a circle at 2 distinct points.
In the applet below, 2 secants are drawn to the circle from the SAME POINT OUTSIDE THE CIRCLE.
These 2 secants intercept the red arc and green arc.
Experiment with the applet below for a few minutes and then answer the questions that follow.
Be sure to move the BIG RED POINTS and BIG GREEN POINTS around to change the measures of the 2 arcs intercepted by these 2 secants.
You can also move the vertices of the two inscribed angles as well. The red inscribed angle intercepts the same red arc that the secant lines intercept. The green inscribed angle intercepts the same green arc the the secant lines intercept.
The purple angle (you see when you drag the slider to the end) is called an angle formed by two secants.
Given what you've just observed, answer the following questions:
Suppose the red arc measures 150 degrees and the green arc measures 80 degrees. If this were so,
1) What would the measure of the red inscribed angle be?
2) What would the measure of the green inscribed angle be?
3) What would the measure of the purple angle be?
Suppose the red arc measured 120 degrees and the green arc measures 30 degrees.
4) What would the measure of the red inscribed angle be?
5) What would the measure of the green inscribed angle be?
6) What would the measure of the purple angle be?
From your observations, describe how to find the measure of an angle formed by two secant rays. Be sure to use the phrase "intercepted arc(s)" at least once in your description. Please be as specific as you can.