A central angle has its point at the circle’s center, so its degree measure tells you what share of the circle its arc covers. Compare the angle with a full turn, then scale the arc length up to the whole circumference. The trap is using the angle’s fraction in the wrong direction: you have the part and need the whole.
Hints
- Hint 1
A central angle starts at the circle’s center. Its degree measure tells you what fraction of the circle the intercepted arc covers. What fraction is of a full turn?
- Hint 2
The arc length measures part of the circle’s curved edge. Once you know that part’s fraction, ask how many copies of it would make the entire circumference.
Step-by-step
Scale the arc up to a full circle
Step 1Find the angle’s share of a full turn
No Desmos needed. The angle gives a direct fraction, and finding the whole takes one multiplication. A central angle has its point at the circle’s center. A full turn is , so the given angle covers one eighth of the circle:
- Step 2
Scale the arc length to the circumference
An arc is the same fraction of the circumference as its central angle is of a full turn. The given arc length, , is one eighth of the circle’s curved edge. To get the whole circumference, use eight copies of that arc: . The circumference of circle is . Choice C.