geometry
posted by jake .
Circle O above has a circumference of 240 cm and arc XW has a length of 60 cm. What is the measure of the central angle associated with arc XW?

geometry 
jai
first we get the ratio of the arclength to circumference:
60 cm / 240 cm = 1/4
since the arc covers 1/4 of the circumference, it also means that it forms 1/4 of the total angle of a circle.
angle of a circle is 360 degrees, thus central angle associated by XW is:
(1/4)*360 = 90 degrees
hope this helps~ :)
Respond to this Question
Similar Questions

geometry
In circle P, arc EN=66, angle GPM=89, and GN is the diameter. Find the measure of angle EGN. The answer is 33ยบ but I'm not sure how you get it. There is a theorm that says the inscribed angle of a circle arc is 1/2 the arc (or one … 
math
Whats the difference between an arc [of a circle]'s length and measure? 
geometry
If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc? 
geometry
If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc? 
geometry
If the arc on a particular circle has an arc length of 14 inches, and the circumference of the circle is 84 inches, what is the angle measure of the arc? 
math advanced functions
a) Determine the measure of the central angle that is formed by an arc length of 5 cm in a circle with a radius of 2.5cm. Express the measure in both radians and degrees, correct to one decimal place. b) Determine the arc length of … 
Geometry
If a central angle of 90 degrees defines an arc on circle R that has the same length as the arc on circle W defined by a 60degree central angle, what is the ratio of the area of circle R to the area of circle W? 
apex geometry
Hannah constructed two similar circles as seen in the image below. If the arc length of the larger circle is , which of the following would be true? 
geometry
A circle has a circumference of 12. It has an arc of length 8/5 What is the central angle of the arc, in degrees? 
Geometry
A circle has a radius of 3 an arc in this circle has a central angle of 20 degrees what is the length of the arc