Inscribed angleCenter angle given
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The angle at the center is given. Find the angle on the circle.
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Find the inscribed angle worksheets
When the angle at the center is given, the angle on the circle is half of it. These free printable worksheets ask for that one direction, eight times a page, so a student can get used to reading the figure before the two directions are mixed.
If they get stuck
Find the inscribed 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 at the center carries a number, such as 130°, and the one on the circle carries a question mark. Half of 130° is 65°, and that is all the arithmetic there is. What takes practice is seeing that the two angles are a pair, because the theorem only applies to angles that stand on the same arc.
Why this sheet works
Some figures look quite different from others. A 30° angle at the center gives a narrow sliver, and a 170° angle almost reaches a straight line across the circle. The rule stays the same in both, and working through the two extremes on a page is a good way to believe it.
How this one works
Center angle 30°, find the angle on the circle
same arc, two angles
center = 2 × circlesocircle = center ÷ 2
30 ÷ 2=15
- 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 center angle is the one given, so this is a halving.
- Half of 30 is 15, so the angle on the circle is 15°.