Inscribed angleEither angle given
Name: Date:
One angle is given. Find the one marked with a question mark.
1 degrees
2 degrees
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8 degrees
Inscribed angle in a circle worksheets
Two angles standing on the same arc: one at the center of the circle, one out on the rim. The one at the center is always twice the other. These free printable worksheets ask for each direction, and mix them.
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Inscribed angle in a circle
The answer key prints on a separate page.
What's on this sheet
This is a theorem rather than a formula, and the difference shows in what a child has to do. There is nothing to measure and nothing to substitute — the whole question is reading which of the two marked angles was given, and then halving or doubling. Which is exactly why a page of one direction is not enough practice: handed the center angle the mistake is doubling, handed the rim angle it is halving, and the mixed page is the one where the figure has to be read first.
Why this sheet works
Both angles are marked on every figure, one with its size and one with a question mark, because the theorem is a statement about a pair. A figure showing one angle would be showing half the question, and the two arcs are drawn at different radii so a 30° angle and a 150° one do not read the same at a glance.
How this one works
One question from this sheet, worked through a step at a time.
Circle angle 25°, find the angle at the center
same arc, two angles
center = 2 × circle
2 × 25=50
- Both marked angles stand on the SAME arc — the two chords and the two radii end at the same two points on the circle. That is what makes them a pair; two angles in a circle that do not share an arc have nothing to say to each other.
- 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 25 is 50, so the angle at the center is 50°.