Angles in a triangle worksheet for Pre-Algebra

In Pre-Algebra the triangle sum is a chance to write and solve a short equation: add the known angles and subtract from 180, or set expressions in x equal to 180 and solve. Right triangles come up too, where the two acute angles share the remaining 90.

Also taught in Geometry, at its own level and with its own examples.

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

Classifying Triangles (Pre-Algebra). 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.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



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 The angles of a triangle are in the ratio $1 : 2 : 6$ . Find the middle-sized angle. Find the value of $x$ . In $△ E G H$ , $m ∠ H = 75^{\circ}$ and $m ∠ G$ is 4 times $m ∠ E$ . Find $m ∠ G$ . Find $x$ . Find the third angle. Find the measure of the angle marked ${(x + 66)}^{\circ}$ . In right $△ Z D G$ , $∠ G$ is the right angle and $m ∠ Z = 22^{\circ}$ . Find $m ∠ D$ . Find the measure of the angle marked ${(4 x - 5)}^{\circ}$ . Find an angle or $x$ with the exterior angle theorem The vertex angle of an isosceles triangle measures $30^{\circ}$ . Find the exterior angle at one of its base angles. Find the measure of the exterior angle. Find the angle marked $x$ . Find $x$ , the measure of the exterior angle. The exterior angle at $B$ of $△ Z C B$ measures $85^{\circ}$ , and $m ∠ Z : m ∠ C = 2 : 3$ . Find $m ∠ Z$ . What is the value of $x$ ? The exterior angle at $U$ of $△ C A U$ measures $50^{\circ}$ , and $m ∠ C = m ∠ A$ . Find $m ∠ C$ . Use the exterior angle theorem to find $x$ . Find the acute angles The acute angles of a right triangle are in the ratio $5 : 13$ . Find each angle. One acute angle of a right triangle is 6 degrees more than 3 times the other. Find each angle. The acute angles of a right triangle differ by $14^{\circ}$ . Find each angle. The acute angles of a right triangle measure ${(6 x - 6)}^{\circ}$ and ${(4 x + 6)}^{\circ}$ . 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
The angles of a triangle are in the ratio $1 : 2 : 6$ . Find the middle-sized angle.
Find the value of $x$ .
In $△ E G H$ , $m ∠ H = 75^{\circ}$ and $m ∠ G$ is 4 times $m ∠ E$ . Find $m ∠ G$ .
Find $x$ .
Find the third angle.
Find the measure of the angle marked ${(x + 66)}^{\circ}$ .
In right $△ Z D G$ , $∠ G$ is the right angle and $m ∠ Z = 22^{\circ}$ . Find $m ∠ D$ .
Find the measure of the angle marked ${(4 x - 5)}^{\circ}$ .

Find an angle or $x$ with the exterior angle theorem
The vertex angle of an isosceles triangle measures $30^{\circ}$ . Find the exterior angle at one of its base angles.
Find the measure of the exterior angle.
Find the angle marked $x$ .
Find $x$ , the measure of the exterior angle.
The exterior angle at $B$ of $△ Z C B$ measures $85^{\circ}$ , and $m ∠ Z : m ∠ C = 2 : 3$ . Find $m ∠ Z$ .
What is the value of $x$ ?
The exterior angle at $U$ of $△ C A U$ measures $50^{\circ}$ , and $m ∠ C = m ∠ A$ . Find $m ∠ C$ .
Use the exterior angle theorem to find $x$ .

Find the acute angles
The acute angles of a right triangle are in the ratio $5 : 13$ . Find each angle.
One acute angle of a right triangle is 6 degrees more than 3 times the other. Find each angle.
The acute angles of a right triangle differ by $14^{\circ}$ . Find each angle.
The acute angles of a right triangle measure ${(6 x - 6)}^{\circ}$ and ${(4 x + 6)}^{\circ}$ . Find each angle.



Sigma Prep · sigmaprep.io/worksheets Name Angles in a TriangleAnswer keyVersion 2 Date Period Find each angle or the value of x. Find $x$ or the missing angle The angles of a triangle are in the ratio $1 : 2 : 6$ . Find the middle-sized angle. $40^{\circ}$ Find the value of $x$ . $12$ In $△ E G H$ , $m ∠ H = 75^{\circ}$ and $m ∠ G$ is 4 times $m ∠ E$ . Find $m ∠ G$ . $84^{\circ}$ Find $x$ . $17$ Find the third angle. $26^{\circ}$ Find the measure of the angle marked ${(x + 66)}^{\circ}$ . $73^{\circ}$ In right $△ Z D G$ , $∠ G$ is the right angle and $m ∠ Z = 22^{\circ}$ . Find $m ∠ D$ . $68^{\circ}$ Find the measure of the angle marked ${(4 x - 5)}^{\circ}$ . $63^{\circ}$ Find an angle or $x$ with the exterior angle theorem The vertex angle of an isosceles triangle measures $30^{\circ}$ . Find the exterior angle at one of its base angles. $105^{\circ}$ Find the measure of the exterior angle. $112^{\circ}$ Find the angle marked $x$ . $99^{\circ}$ Find $x$ , the measure of the exterior angle. $122^{\circ}$ The exterior angle at $B$ of $△ Z C B$ measures $85^{\circ}$ , and $m ∠ Z : m ∠ C = 2 : 3$ . Find $m ∠ Z$ . $34^{\circ}$ What is the value of $x$ ? $18$ The exterior angle at $U$ of $△ C A U$ measures $50^{\circ}$ , and $m ∠ C = m ∠ A$ . Find $m ∠ C$ . $25^{\circ}$ Use the exterior angle theorem to find $x$ . $10$ Find the acute angles The acute angles of a right triangle are in the ratio $5 : 13$ . Find each angle. $25^{\circ}$ and $65^{\circ}$ One acute angle of a right triangle is 6 degrees more than 3 times the other. Find each angle. $21^{\circ}$ and $69^{\circ}$ The acute angles of a right triangle differ by $14^{\circ}$ . Find each angle. $38^{\circ}$ and $52^{\circ}$ The acute angles of a right triangle measure ${(6 x - 6)}^{\circ}$ and ${(4 x + 6)}^{\circ}$ . Find each angle. $48^{\circ}$ and $42^{\circ}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Angles in a TriangleAnswer keyVersion 2

Date Period

Find each angle or the value of x.

Find $x$ or the missing angle
The angles of a triangle are in the ratio $1 : 2 : 6$ . Find the middle-sized angle. $40^{\circ}$
Find the value of $x$ . $12$
In $△ E G H$ , $m ∠ H = 75^{\circ}$ and $m ∠ G$ is 4 times $m ∠ E$ . Find $m ∠ G$ . $84^{\circ}$
Find $x$ . $17$
Find the third angle. $26^{\circ}$
Find the measure of the angle marked ${(x + 66)}^{\circ}$ . $73^{\circ}$
In right $△ Z D G$ , $∠ G$ is the right angle and $m ∠ Z = 22^{\circ}$ . Find $m ∠ D$ . $68^{\circ}$
Find the measure of the angle marked ${(4 x - 5)}^{\circ}$ . $63^{\circ}$

Find an angle or $x$ with the exterior angle theorem
The vertex angle of an isosceles triangle measures $30^{\circ}$ . Find the exterior angle at one of its base angles. $105^{\circ}$
Find the measure of the exterior angle. $112^{\circ}$
Find the angle marked $x$ . $99^{\circ}$
Find $x$ , the measure of the exterior angle. $122^{\circ}$
The exterior angle at $B$ of $△ Z C B$ measures $85^{\circ}$ , and $m ∠ Z : m ∠ C = 2 : 3$ . Find $m ∠ Z$ . $34^{\circ}$
What is the value of $x$ ? $18$
The exterior angle at $U$ of $△ C A U$ measures $50^{\circ}$ , and $m ∠ C = m ∠ A$ . Find $m ∠ C$ . $25^{\circ}$
Use the exterior angle theorem to find $x$ . $10$

Find the acute angles
The acute angles of a right triangle are in the ratio $5 : 13$ . Find each angle. $25^{\circ}$ and $65^{\circ}$
One acute angle of a right triangle is 6 degrees more than 3 times the other. Find each angle. $21^{\circ}$ and $69^{\circ}$
The acute angles of a right triangle differ by $14^{\circ}$ . Find each angle. $38^{\circ}$ and $52^{\circ}$
The acute angles of a right triangle measure ${(6 x - 6)}^{\circ}$ and ${(4 x + 6)}^{\circ}$ . Find each angle. $48^{\circ}$ and $42^{\circ}$

How to do these

The angles of a triangle are $x^{\circ}$ , ${(x + 20)}^{\circ}$ and $2 x^{\circ}$ . Find the largest angle

The three angles add to 180: 4x + 20 = 180.
Subtract 20 and divide by 4: x = 40.
The angles are 40, 60 and 80.

The answer is $80^{\circ}$ .

Where students go wrong

Stopping at x. The question usually asks for an angle, so once x = 40 you still have to put it back into each expression, and the three angles should add to 180 as a check.

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.

Pre-Algebra is usually taken around 7th or 8th 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 Pre-Algebra

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