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?

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~ :)

To find the measure of the central angle associated with arc XW, we can use the formula:

Central Angle Measure = (Arc Length / Circumference) * 360 degrees

Given that arc XW has a length of 60 cm and the circle has a circumference of 240 cm, we can substitute these values into the formula:

Central Angle Measure = (60 cm / 240 cm) * 360 degrees

Simplifying the expression:

Central Angle Measure = (1/4) * 360 degrees

Central Angle Measure = 90 degrees

Therefore, the measure of the central angle associated with arc XW is 90 degrees.