Inscribed angles worksheet

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, and two angles standing on the same arc are equal. In a quadrilateral drawn inside a circle, opposite angles add to 180.

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Sigma Prep · sigmaprep.io/worksheets Name Inscribed Angles Date Period Find each measure. Use inscribed angles Find the angle marked $x$ . Find the arc marked $x$ . Find the angle marked $x$ . Find the arc marked $x$ . Find the angle marked $x$ . Solve with two inscribed angles Find the value of $x$ . Solve for $x$ . Find $x$ . Solve for $x$ . Find $x$ . Use inscribed quadrilaterals What is $m ∠ B$ ? Find the measure of the angle marked $x$ . Find $m ∠ B$ . Find $m ∠ C$ . Find $m ∠ D$ . Use an angle in a semicircle $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 14)}^{\circ}$ . Find $x$ . $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(7 x - 15)}^{\circ}$ . Find $x$ . $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 10)}^{\circ}$ . Find $x$ . $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(6 x - 6)}^{\circ}$ . Find $x$ . $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(9 x + 54)}^{\circ}$ . Find $x$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inscribed Angles

Date Period

Find each measure.

Use inscribed angles
Find the angle marked $x$ .
Find the arc marked $x$ .
Find the angle marked $x$ .
Find the arc marked $x$ .
Find the angle marked $x$ .

Solve with two inscribed angles
Find the value of $x$ .
Solve for $x$ .
Find $x$ .
Solve for $x$ .
Find $x$ .

Use inscribed quadrilaterals
What is $m ∠ B$ ?
Find the measure of the angle marked $x$ .
Find $m ∠ B$ .
Find $m ∠ C$ .
Find $m ∠ D$ .

Use an angle in a semicircle
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 14)}^{\circ}$ . Find $x$ .
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(7 x - 15)}^{\circ}$ . Find $x$ .
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 10)}^{\circ}$ . Find $x$ .
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(6 x - 6)}^{\circ}$ . Find $x$ .
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(9 x + 54)}^{\circ}$ . Find $x$ .



Sigma Prep · sigmaprep.io/worksheets Name Inscribed AnglesAnswer keyVersion 1 Date Period Find each measure. Use inscribed angles Find the angle marked $x$ . $45^{\circ}$ Find the arc marked $x$ . $80^{\circ}$ Find the angle marked $x$ . $32^{\circ}$ Find the arc marked $x$ . $120^{\circ}$ Find the angle marked $x$ . $39^{\circ}$ Solve with two inscribed angles Find the value of $x$ . $17$ Solve for $x$ . $14$ Find $x$ . $11$ Solve for $x$ . $10$ Find $x$ . $13$ Use inscribed quadrilaterals What is $m ∠ B$ ? $63^{\circ}$ Find the measure of the angle marked $x$ . $58^{\circ}$ Find $m ∠ B$ . $111^{\circ}$ Find $m ∠ C$ . $73^{\circ}$ Find $m ∠ D$ . $77^{\circ}$ Use an angle in a semicircle $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 14)}^{\circ}$ . Find $x$ . $19$ $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(7 x - 15)}^{\circ}$ . Find $x$ . $15$ $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 10)}^{\circ}$ . Find $x$ . $20$ $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(6 x - 6)}^{\circ}$ . Find $x$ . $16$ $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(9 x + 54)}^{\circ}$ . Find $x$ . $4$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inscribed AnglesAnswer keyVersion 1

Date Period

Find each measure.

Use inscribed angles
Find the angle marked $x$ . $45^{\circ}$
Find the arc marked $x$ . $80^{\circ}$
Find the angle marked $x$ . $32^{\circ}$
Find the arc marked $x$ . $120^{\circ}$
Find the angle marked $x$ . $39^{\circ}$

Solve with two inscribed angles
Find the value of $x$ . $17$
Solve for $x$ . $14$
Find $x$ . $11$
Solve for $x$ . $10$
Find $x$ . $13$

Use inscribed quadrilaterals
What is $m ∠ B$ ? $63^{\circ}$
Find the measure of the angle marked $x$ . $58^{\circ}$
Find $m ∠ B$ . $111^{\circ}$
Find $m ∠ C$ . $73^{\circ}$
Find $m ∠ D$ . $77^{\circ}$

Use an angle in a semicircle
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 14)}^{\circ}$ . Find $x$ . $19$
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(7 x - 15)}^{\circ}$ . Find $x$ . $15$
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(4 x + 10)}^{\circ}$ . Find $x$ . $20$
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(6 x - 6)}^{\circ}$ . Find $x$ . $16$
$\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ A C B = {(9 x + 54)}^{\circ}$ . Find $x$ . $4$

How to do these

An inscribed angle cuts off an arc of $116^{\circ}$ . Find the angle

An inscribed angle is half its arc.
Half of 116 is 58.

The answer is $58^{\circ}$ .

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.

What you can put on this worksheet

Inscribed angles: Find the arc marked $x$ . — a circle with an inscribed angle, labeled 41°, x → $82^{\circ}$
Two inscribed angles on one arc: Find the value of $x$ . — two inscribed angles on the same arc, (3x + 30)° and (x + 46)° → $8$
Quadrilaterals inscribed in a circle: Find $m ∠ C$ . — a quadrilateral abcd inscribed in a circle, labeled A, 92°, B, C, D, 86° → $88^{\circ}$
An angle in a semicircle: $\overline{A B}$ is a diameter of the circle and $C$ is on the circle. $m ∠ C B A = 47^{\circ}$ . Find $m ∠ C A B$ . → $43^{\circ}$
Is it an inscribed angle? Name its arc: Is $∠ U T S$ an inscribed angle? If it is, name the arc it cuts off. — a circle with an angle drawn from a point to two points on the circle, labeled U, S, T → No
Inscribed quadrilateral with x and y: Find $x$ and $y$ . — a quadrilateral abcd inscribed in a circle, labeled A, B, C, D → $x = 10$ , $y = 3$
A triangle drawn on a diameter: $\overline{A B}$ is a diameter. Find $m \overset{⌢}{BC}$ . — a circle with points, chords and arcs, labeled 40°, A, B, C, O → $100^{\circ}$
The arc from 360 first, or written in x: Find $x$ . — a circle with points, chords and arcs, labeled 130°, P, A, B → $3$

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.

You pick from 8: inscribed angles, two inscribed angles on one arc, quadrilaterals inscribed in a circle, an angle in a semicircle, is it an inscribed angle? name its arc, inscribed quadrilateral with x and y, a triangle drawn on a diameter and the arc from 360 first, or written in x. Tick as many as you want and set how many of each, or let it spread them evenly.

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.

Inscribed angles worksheet

Select your difficulty

Use inscribed angles

Solve with two inscribed angles

Use inscribed quadrilaterals

Use an angle in a semicircle

Use inscribed angles

Solve with two inscribed angles

Use inscribed quadrilaterals

Use an angle in a semicircle

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these inscribed angles worksheets free?+

Do the inscribed angles worksheets come with an answer key?+

Are these inscribed angles worksheets printable?+

What grade are these inscribed angles worksheets for?+

Can I get a different version of the same inscribed angles worksheet?+

Is this a free alternative to Kuta Software for inscribed angles?+

Can I choose how hard the inscribed angles questions are?+

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What do students get wrong with inscribed angles?+