Angle relationships worksheet for Geometry

Two angles that make a right angle are complementary; two that make a straight line are supplementary. Every level mixes pairs given as numbers, in x or as a ratio with angles round a point, three lines through one point, and naming the relationship.

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

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

Vertical Angles and Linear Pairs (Geometry). Opposite angles are equal, neighbors add to 180.

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 Angle Relationships Date Period Find each angle, or name each relationship. Solve with complementary angles Two angles are complementary. One measures $27^{\circ}$ . Find the other. The angles are complementary. Find the unknown angle. Two complementary angles differ by $50^{\circ}$ . Find the smaller angle. The measures of two complementary angles are ${(4 x - 10)}^{\circ}$ and ${(4 x - 12)}^{\circ}$ . Find $x$ . Solve with supplementary angles The supplement of an angle is $21^{\circ}$ more than twice the angle. The angle measures $x^{\circ}$ . Find $x$ . Solve for $x$ . Two angles are supplementary. One measures $19^{\circ}$ . Find the other. Find the missing angle. Find angles in a given ratio The angles are complementary. Find the larger angle. Two supplementary angles are in the ratio $1 : 11$ . Find the smaller one. Two angles form a linear pair, and their measures are in the ratio $2 : 13$ . Find the larger angle. Name the angle relationship Give the most specific name. $m ∠ 1 = 65^{\circ}$ and $m ∠ 2 = 25^{\circ}$ . They do not share a side. Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side and do not overlap. $m ∠ 1 = 21^{\circ}$ , $m ∠ 2 = 59^{\circ}$ . Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side, and their other sides form a straight line. Find angles around a point Several rays start at one point. What is $x$ ? The angles fill the space all the way around the point. Find the angle marked $5 x^{\circ}$ . Together the marked angles go once around the point. How big is the angle marked ${(4 x + 41)}^{\circ}$ ? Find angles where three lines meet What is the measure of the angle marked ${(5 x + 4)}^{\circ}$ ? The lines cross at one point, making six angles. Solve for $x$ . Three lines cross at one point. Find $x$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Angle Relationships

Date Period

Find each angle, or name each relationship.

Solve with complementary angles
Two angles are complementary. One measures $27^{\circ}$ . Find the other.
The angles are complementary. Find the unknown angle.
Two complementary angles differ by $50^{\circ}$ . Find the smaller angle.
The measures of two complementary angles are ${(4 x - 10)}^{\circ}$ and ${(4 x - 12)}^{\circ}$ . Find $x$ .

Solve with supplementary angles
The supplement of an angle is $21^{\circ}$ more than twice the angle. The angle measures $x^{\circ}$ . Find $x$ .
Solve for $x$ .
Two angles are supplementary. One measures $19^{\circ}$ . Find the other.
Find the missing angle.

Find angles in a given ratio
The angles are complementary. Find the larger angle.
Two supplementary angles are in the ratio $1 : 11$ . Find the smaller one.
Two angles form a linear pair, and their measures are in the ratio $2 : 13$ . Find the larger angle.

Name the angle relationship
Give the most specific name. $m ∠ 1 = 65^{\circ}$ and $m ∠ 2 = 25^{\circ}$ . They do not share a side.
Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side and do not overlap. $m ∠ 1 = 21^{\circ}$ , $m ∠ 2 = 59^{\circ}$ .
Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side, and their other sides form a straight line.

Find angles around a point
Several rays start at one point. What is $x$ ?
The angles fill the space all the way around the point. Find the angle marked $5 x^{\circ}$ .
Together the marked angles go once around the point. How big is the angle marked ${(4 x + 41)}^{\circ}$ ?

Find angles where three lines meet
What is the measure of the angle marked ${(5 x + 4)}^{\circ}$ ?
The lines cross at one point, making six angles. Solve for $x$ .
Three lines cross at one point. Find $x$ .



Sigma Prep · sigmaprep.io/worksheets Name Angle RelationshipsAnswer keyVersion 1 Date Period Find each angle, or name each relationship. Solve with complementary angles Two angles are complementary. One measures $27^{\circ}$ . Find the other. $63^{\circ}$ The angles are complementary. Find the unknown angle. $62^{\circ}$ Two complementary angles differ by $50^{\circ}$ . Find the smaller angle. $20^{\circ}$ The measures of two complementary angles are ${(4 x - 10)}^{\circ}$ and ${(4 x - 12)}^{\circ}$ . Find $x$ . $14$ Solve with supplementary angles The supplement of an angle is $21^{\circ}$ more than twice the angle. The angle measures $x^{\circ}$ . Find $x$ . $53$ Solve for $x$ . $15$ Two angles are supplementary. One measures $19^{\circ}$ . Find the other. $161^{\circ}$ Find the missing angle. $50^{\circ}$ Find angles in a given ratio The angles are complementary. Find the larger angle. ${67.5}^{\circ}$ Two supplementary angles are in the ratio $1 : 11$ . Find the smaller one. $15^{\circ}$ Two angles form a linear pair, and their measures are in the ratio $2 : 13$ . Find the larger angle. $156^{\circ}$ Name the angle relationship Give the most specific name. $m ∠ 1 = 65^{\circ}$ and $m ∠ 2 = 25^{\circ}$ . They do not share a side.Complementary Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side and do not overlap. $m ∠ 1 = 21^{\circ}$ , $m ∠ 2 = 59^{\circ}$ .Adjacent Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side, and their other sides form a straight line.Linear pair Find angles around a point Several rays start at one point. What is $x$ ? $5$ The angles fill the space all the way around the point. Find the angle marked $5 x^{\circ}$ . $200^{\circ}$ Together the marked angles go once around the point. How big is the angle marked ${(4 x + 41)}^{\circ}$ ? $93^{\circ}$ Find angles where three lines meet What is the measure of the angle marked ${(5 x + 4)}^{\circ}$ ? $74^{\circ}$ The lines cross at one point, making six angles. Solve for $x$ . $10$ Three lines cross at one point. Find $x$ . $40$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Angle RelationshipsAnswer keyVersion 1

Date Period

Find each angle, or name each relationship.

Solve with complementary angles
Two angles are complementary. One measures $27^{\circ}$ . Find the other. $63^{\circ}$
The angles are complementary. Find the unknown angle. $62^{\circ}$
Two complementary angles differ by $50^{\circ}$ . Find the smaller angle. $20^{\circ}$
The measures of two complementary angles are ${(4 x - 10)}^{\circ}$ and ${(4 x - 12)}^{\circ}$ . Find $x$ . $14$

Solve with supplementary angles
The supplement of an angle is $21^{\circ}$ more than twice the angle. The angle measures $x^{\circ}$ . Find $x$ . $53$
Solve for $x$ . $15$
Two angles are supplementary. One measures $19^{\circ}$ . Find the other. $161^{\circ}$
Find the missing angle. $50^{\circ}$

Find angles in a given ratio
The angles are complementary. Find the larger angle. ${67.5}^{\circ}$
Two supplementary angles are in the ratio $1 : 11$ . Find the smaller one. $15^{\circ}$
Two angles form a linear pair, and their measures are in the ratio $2 : 13$ . Find the larger angle. $156^{\circ}$

Name the angle relationship
Give the most specific name. $m ∠ 1 = 65^{\circ}$ and $m ∠ 2 = 25^{\circ}$ . They do not share a side.Complementary
Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side and do not overlap. $m ∠ 1 = 21^{\circ}$ , $m ∠ 2 = 59^{\circ}$ .Adjacent
Give the most specific name. $∠ 1$ and $∠ 2$ share a vertex and a side, and their other sides form a straight line.Linear pair

Find angles around a point
Several rays start at one point. What is $x$ ? $5$
The angles fill the space all the way around the point. Find the angle marked $5 x^{\circ}$ . $200^{\circ}$
Together the marked angles go once around the point. How big is the angle marked ${(4 x + 41)}^{\circ}$ ? $93^{\circ}$

Find angles where three lines meet
What is the measure of the angle marked ${(5 x + 4)}^{\circ}$ ? $74^{\circ}$
The lines cross at one point, making six angles. Solve for $x$ . $10$
Three lines cross at one point. Find $x$ . $40$

How to do these

Find the complement of $37^{\circ}$

Complementary angles add to 90.
90 minus 37.

The answer is $53^{\circ}$ .

Where students go wrong

Calling two angles vertical because they look equal. Vertical angles sit opposite each other where two lines cross; angles that only share a side are adjacent, and their measures add instead.

Also called angle pairs, angles around a point or angle pair relationships.

What you can put on this worksheet

Complementary angles: The angles are complementary. Find the unknown angle. — two angles, x and 50°, on a shared ray → $40^{\circ}$
Supplementary angles: The angles are supplementary. Find the unknown angle. — two angles, x and 101°, on a straight line → $79^{\circ}$
Two angles in a ratio: Two supplementary angles are in the ratio $1 : 8$ . Find the smaller one. → $20^{\circ}$
Name the relationship: Give the most specific name. $m ∠ 1 = 49^{\circ}$ and $m ∠ 2 = 41^{\circ}$ . They do not share a side. → Complementary
Angles round a point make 360: Together the marked angles go once around the point. Find $x$ . — rays from one point, with the angles between them marked, labeled 53°, 87°, x°, 146° → $74$
Three lines through one point: What is $x$ ? — rays from one point, with the angles between them marked, labeled 67° → $3$
Name the relationship from a drawing: Name the relationship between $∠ 1$ and $∠ 2$ : vertical angles, a linear pair, complementary, or only adjacent. — two angles that share a vertex, labeled 1, 2 → Complementary

Questions about these worksheets

Yes. Every angle relationships 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 angle relationships 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 three 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: complementary angles, supplementary angles, two angles in a ratio, name the relationship, angles round a point make 360, three lines through one point and name the relationship from a drawing. Tick as many as you want and set how many of each, or let it spread them evenly.

Swapping the two words. Complementary is the smaller total, 90, and supplementary is 180. A quick check: a complement only exists for an angle under 90.

Angle relationships worksheet for Geometry

Select your difficulty

Solve with complementary angles

Solve with supplementary angles

Find angles in a given ratio

Name the angle relationship

Find angles around a point

Find angles where three lines meet

Solve with complementary angles

Solve with supplementary angles

Find angles in a given ratio

Name the angle relationship

Find angles around a point

Find angles where three lines meet

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these angle relationships worksheets free?+

Do the angle relationships worksheets come with an answer key?+

Are these angle relationships worksheets printable?+

What grade are these angle relationships worksheets for?+

Can I get a different version of the same angle relationships worksheet?+

Is this a free alternative to Kuta Software for angle relationships?+

Can I choose how hard the angle relationships questions are?+

What kinds of question are on a angle relationships worksheet?+

What do students get wrong with angle relationships?+