SOLUTION: The angle formed by two secants intersecting on the exterior of the circle measure 95 degrees. One of the intercepted arcs is 220 degrees. Find the measure of the other arc. Tha

Algebra.Com
Question 1205670: The angle formed by two secants intersecting on the exterior of the circle measure 95 degrees. One of the intercepted arcs is 220 degrees. Find the measure of the other arc.
Thank you! =)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52886)   (Show Source): You can put this solution on YOUR website!
.
The angle formed by two secants intersecting on the exterior of the circle measure 95 degrees.
One of the intercepted arcs is 220 degrees. Find the measure of the other arc.
Thank you! =)
~~~~~~~~~~~~~~~~~~~~~~~~ 

Let the arcs be  and .


Then from the problem

    95 =     (1)

     = 220.           (2)


Substitute expression (2) for   into equation (1).
You will get then

    95 = ,

    95*2 = 220 - ,

     = 220 - 95*2 = 220 - 190 = 30.


ANSWER.  The other arc is 30 degrees.

Solved.



Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


The operative principle you want to learn here is that the measure of the angle formed by two secants and/or tangents to a circle is half the difference between the measures of the two arcs of the circle they cut off.

Then do the calculations as shown by the other tutor.
RELATED QUESTIONS

The angle formed by two secants intersecting in the exterior of the circle measure 86.One (answered by vksarvepalli)
I have a few questions I need answered. I think I know how to do them, but I'm not sure.... (answered by lynnlo)
The measure of the angke formed by two tangents to a circle is 80 degrees. Find the... (answered by ikleyn,MathTherapy)
Solve the problem and show the solutions. The measure of the angle formed by two... (answered by greenestamps,ikleyn)
the angle formed by two tangents drawn to a circle from the same external point measures... (answered by ikleyn)
Find the length of the arc, S, on a circle of radius 7 feet intercepted by a central... (answered by lwsshak3)
Find the length of arc , S, on a circle of radius 3 meters intercepted by a central angle (answered by ankor@dixie-net.com)
The length of the arc intercepted by a central angle of 2 radians in a circle of radius... (answered by macston)
By how much does the arc intercepted by a central angle of 38 degrees exceed the chord... (answered by KMST,MathTherapy)