Angles in a triangle worksheet for Geometry

The three angles of any triangle add to 180. An exterior angle equals the two interior angles it is not touching, which follows from the same fact.

Also taught in Pre-Algebra, at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Classifying Triangles (Geometry). Scalene, isosceles, equilateral. Acute, right, obtuse.
Isosceles and Equilateral Triangles (Geometry). Equal sides mean equal angles.
The Exterior Angle Theorem (Geometry). An exterior angle equals the two far interior ones.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Angles in a Triangle Date Period Find each angle or the value of x. Find $x$ or the missing angle In right $△ A M Z$ , $∠ Z$ is the right angle and $m ∠ A = 52^{\circ}$ . Find $m ∠ M$ . Find the measure of the angle marked ${(x + 97)}^{\circ}$ . Find the third angle. Find the value of $x$ . The angles of a triangle are in the ratio $1 : 2 : 3$ . Find the middle-sized angle. Find the measure of the angle marked ${(2 x + 39)}^{\circ}$ . In isosceles $△ H E B$ , $H E = H B$ and $m ∠ H = 58^{\circ}$ . Find $m ∠ E$ . Find the value of $x$ . Find an angle or $x$ with the exterior angle theorem The exterior angle at $L$ of $△ K Z L$ measures $82^{\circ}$ , and $m ∠ K = m ∠ Z$ . Find $m ∠ K$ . Find $x$ . Find the exterior angle. Find the angle marked $x$ . The exterior angle at $W$ of $△ T H W$ measures $98^{\circ}$ , and $m ∠ T : m ∠ H = 2 : 5$ . Find $m ∠ T$ . Find the measure of the exterior angle. The exterior angle at $R$ of $△ L E R$ measures $147^{\circ}$ , and $m ∠ L = 97^{\circ}$ . Find $m ∠ E$ . Use the exterior angle theorem to find $x$ . Find the acute angles The acute angles of a right triangle differ by $24^{\circ}$ . Find each angle. The acute angles of a right triangle are in the ratio $1 : 2$ . Find each angle. The acute angles of a right triangle measure $4 x^{\circ}$ and ${(2 x + 18)}^{\circ}$ . Find each angle. One acute angle of a right triangle is 14 degrees less than 3 times the other. Find each angle. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Angles in a Triangle

Date Period

Find each angle or the value of x.

Find $x$ or the missing angle
In right $△ A M Z$ , $∠ Z$ is the right angle and $m ∠ A = 52^{\circ}$ . Find $m ∠ M$ .
Find the measure of the angle marked ${(x + 97)}^{\circ}$ .
Find the third angle.
Find the value of $x$ .
The angles of a triangle are in the ratio $1 : 2 : 3$ . Find the middle-sized angle.
Find the measure of the angle marked ${(2 x + 39)}^{\circ}$ .
In isosceles $△ H E B$ , $H E = H B$ and $m ∠ H = 58^{\circ}$ . Find $m ∠ E$ .
Find the value of $x$ .

Find an angle or $x$ with the exterior angle theorem
The exterior angle at $L$ of $△ K Z L$ measures $82^{\circ}$ , and $m ∠ K = m ∠ Z$ . Find $m ∠ K$ .
Find $x$ .
Find the exterior angle.
Find the angle marked $x$ .
The exterior angle at $W$ of $△ T H W$ measures $98^{\circ}$ , and $m ∠ T : m ∠ H = 2 : 5$ . Find $m ∠ T$ .
Find the measure of the exterior angle.
The exterior angle at $R$ of $△ L E R$ measures $147^{\circ}$ , and $m ∠ L = 97^{\circ}$ . Find $m ∠ E$ .
Use the exterior angle theorem to find $x$ .

Find the acute angles
The acute angles of a right triangle differ by $24^{\circ}$ . Find each angle.
The acute angles of a right triangle are in the ratio $1 : 2$ . Find each angle.
The acute angles of a right triangle measure $4 x^{\circ}$ and ${(2 x + 18)}^{\circ}$ . Find each angle.
One acute angle of a right triangle is 14 degrees less than 3 times the other. Find each angle.



Sigma Prep · sigmaprep.io/worksheets Name Angles in a TriangleAnswer keyVersion 1 Date Period Find each angle or the value of x. Find $x$ or the missing angle In right $△ A M Z$ , $∠ Z$ is the right angle and $m ∠ A = 52^{\circ}$ . Find $m ∠ M$ . $38^{\circ}$ Find the measure of the angle marked ${(x + 97)}^{\circ}$ . $109^{\circ}$ Find the third angle. $44^{\circ}$ Find the value of $x$ . $18$ The angles of a triangle are in the ratio $1 : 2 : 3$ . Find the middle-sized angle. $60^{\circ}$ Find the measure of the angle marked ${(2 x + 39)}^{\circ}$ . $57^{\circ}$ In isosceles $△ H E B$ , $H E = H B$ and $m ∠ H = 58^{\circ}$ . Find $m ∠ E$ . $61^{\circ}$ Find the value of $x$ . $17$ Find an angle or $x$ with the exterior angle theorem The exterior angle at $L$ of $△ K Z L$ measures $82^{\circ}$ , and $m ∠ K = m ∠ Z$ . Find $m ∠ K$ . $41^{\circ}$ Find $x$ . $13$ Find the exterior angle. $95^{\circ}$ Find the angle marked $x$ . $65^{\circ}$ The exterior angle at $W$ of $△ T H W$ measures $98^{\circ}$ , and $m ∠ T : m ∠ H = 2 : 5$ . Find $m ∠ T$ . $28^{\circ}$ Find the measure of the exterior angle. $116^{\circ}$ The exterior angle at $R$ of $△ L E R$ measures $147^{\circ}$ , and $m ∠ L = 97^{\circ}$ . Find $m ∠ E$ . $50^{\circ}$ Use the exterior angle theorem to find $x$ . $11$ Find the acute angles The acute angles of a right triangle differ by $24^{\circ}$ . Find each angle. $33^{\circ}$ and $57^{\circ}$ The acute angles of a right triangle are in the ratio $1 : 2$ . Find each angle. $30^{\circ}$ and $60^{\circ}$ The acute angles of a right triangle measure $4 x^{\circ}$ and ${(2 x + 18)}^{\circ}$ . Find each angle. $48^{\circ}$ and $42^{\circ}$ One acute angle of a right triangle is 14 degrees less than 3 times the other. Find each angle. $26^{\circ}$ and $64^{\circ}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Angles in a TriangleAnswer keyVersion 1

Date Period

Find each angle or the value of x.

Find $x$ or the missing angle
In right $△ A M Z$ , $∠ Z$ is the right angle and $m ∠ A = 52^{\circ}$ . Find $m ∠ M$ . $38^{\circ}$
Find the measure of the angle marked ${(x + 97)}^{\circ}$ . $109^{\circ}$
Find the third angle. $44^{\circ}$
Find the value of $x$ . $18$
The angles of a triangle are in the ratio $1 : 2 : 3$ . Find the middle-sized angle. $60^{\circ}$
Find the measure of the angle marked ${(2 x + 39)}^{\circ}$ . $57^{\circ}$
In isosceles $△ H E B$ , $H E = H B$ and $m ∠ H = 58^{\circ}$ . Find $m ∠ E$ . $61^{\circ}$
Find the value of $x$ . $17$

Find an angle or $x$ with the exterior angle theorem
The exterior angle at $L$ of $△ K Z L$ measures $82^{\circ}$ , and $m ∠ K = m ∠ Z$ . Find $m ∠ K$ . $41^{\circ}$
Find $x$ . $13$
Find the exterior angle. $95^{\circ}$
Find the angle marked $x$ . $65^{\circ}$
The exterior angle at $W$ of $△ T H W$ measures $98^{\circ}$ , and $m ∠ T : m ∠ H = 2 : 5$ . Find $m ∠ T$ . $28^{\circ}$
Find the measure of the exterior angle. $116^{\circ}$
The exterior angle at $R$ of $△ L E R$ measures $147^{\circ}$ , and $m ∠ L = 97^{\circ}$ . Find $m ∠ E$ . $50^{\circ}$
Use the exterior angle theorem to find $x$ . $11$

Find the acute angles
The acute angles of a right triangle differ by $24^{\circ}$ . Find each angle. $33^{\circ}$ and $57^{\circ}$
The acute angles of a right triangle are in the ratio $1 : 2$ . Find each angle. $30^{\circ}$ and $60^{\circ}$
The acute angles of a right triangle measure $4 x^{\circ}$ and ${(2 x + 18)}^{\circ}$ . Find each angle. $48^{\circ}$ and $42^{\circ}$
One acute angle of a right triangle is 14 degrees less than 3 times the other. Find each angle. $26^{\circ}$ and $64^{\circ}$

How to do these

Two angles of a triangle are $52^{\circ}$ and $61^{\circ}$ . Find the third

All three add to 180.
52 plus 61 is 113.

The answer is $67^{\circ}$ .

Where students go wrong

Using 360 instead of 180. That is the sum for a quadrilateral. The other slip is on exterior angles: it equals the two remote interior angles, not all three.

Also called triangle sum theorem or angle sum of a triangle.

What you can put on this worksheet

The third angle: In right $△ N T B$ , $∠ B$ is the right angle and $m ∠ N = 49^{\circ}$ . Find $m ∠ T$ . → $41^{\circ}$
Exterior angles: Two interior angles of a triangle measure $67^{\circ}$ and $40^{\circ}$ . Find the exterior angle at the third corner. → $107^{\circ}$
Angles written in x: Find the value of $x$ . — a triangle with its angles written in terms of x → $3$
Exterior angles written in x: What is the value of $x$ ? — a triangle with one side extended to show an exterior angle, labeled 69°, 54° → $3$
The acute angles of a right triangle: One acute angle of a right triangle is twice the other. Find each angle. → $30^{\circ}$ and $60^{\circ}$
Exterior angles at two corners: Find the third exterior angle, $x$ . — a triangle with sides carried on past its corners to show exterior angles, labeled x, 120°, 119° → $121^{\circ}$
Two triangles meeting at a crossing: Two segments cross to make two triangles. Find $x$ . — two triangles meeting where two segments cross, labeled 47°, 73°, x°, 62° → $58$

Questions about these worksheets

Yes. Every angles in a triangle 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 angles in a triangle 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 7: the third angle, exterior angles, angles written in x, exterior angles written in x, the acute angles of a right triangle, exterior angles at two corners and two triangles meeting at a crossing. Tick as many as you want and set how many of each, or let it spread them evenly.

Using 360 instead of 180. That is the sum for a quadrilateral. The other slip is on exterior angles: it equals the two remote interior angles, not all three.

Angles in a triangle worksheet for Geometry

Select your difficulty

Find xxx or the missing angle

Find an angle or xxx with the exterior angle theorem

Find the acute angles

Find xxx or the missing angle

Find an angle or xxx with the exterior angle theorem

Find the acute angles

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these angles in a triangle worksheets free?+

Do the angles in a triangle worksheets come with an answer key?+

Are these angles in a triangle worksheets printable?+

What grade are these angles in a triangle worksheets for?+

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

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

Can I choose how hard the angles in a triangle questions are?+

What kinds of question are on a angles in a triangle worksheet?+

What do students get wrong with angles in a triangle?+

Find $x$ or the missing angle

Find an angle or $x$ with the exterior angle theorem

Find $x$ or the missing angle

Find an angle or $x$ with the exterior angle theorem