An angle with its point on the circle is half the arc it cuts off, which is also half the central angle standing on that same arc. Every angle in a semicircle is a right angle for exactly this reason.
An inscribed angle cuts off an arc of 116∘. Find the angle
An inscribed angle is half its arc.
Half of 116 is 58.
The answer is 58∘.
Where students go wrong
Doubling instead of halving. The arc is always the larger number and the inscribed angle the smaller, so an answer bigger than the arc means the rule has been used upside down.
Also called inscribed angle theorem, angles in a circle or central and inscribed angles.
Questions about these worksheets
Yes. Every inscribed angles sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the inscribed angles questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Doubling instead of halving. The arc is always the larger number and the inscribed angle the smaller, so an answer bigger than the arc means the rule has been used upside down.