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.
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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(52879) (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! =)
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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.
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.
