Inscribed angleCircle angle given
Name: Date:
The angle on the circle is given. Find the angle at the center.
1 degrees
2 degrees
3 degrees
4 degrees
5 degrees
6 degrees
7 degrees
8 degrees
Find the central angle worksheets
When the angle on the circle is given, the angle at the center is twice as big. These free printable worksheets ask for that one direction, eight times a page: a 65° angle on the circle stands on the same arc as a 130° angle at the center.
If they get stuck
Find the central angle
The answer key prints on a separate page.
What's on this sheet
Each circle has two angles standing on the same arc. The one on the circle carries a number, and the one at the center carries a question mark. The question is the reverse of the more common one, and that is why it gets its own page. A student who has only ever halved will halve here as well, and 65° turns into 32.5° on the paper.
Why this sheet works
A decimal like that is a useful warning, because every answer here is a whole number. The central angle is also the bigger of the pair, and it should look bigger. Asking which angle looks wider before doing any arithmetic is a quick habit that catches this mistake.
How this one works
Circle angle 15°, find the angle at the center
same arc, two angles
center = 2 × circle
2 × 15=30
- Both marked angles stand on the same arc — the two chords and the two radii end at the same two points on the circle.
- The angle at the center is always twice the one on the circle, wherever on the far arc that point sits. Here the circle angle is the one given, so this is a doubling.
- Twice 15 is 30, so the angle at the center is 30°.