Worksheets · Pre-Algebra

Angle relationships worksheet for Pre-Algebra

In Pre-Algebra angle relationships come in pairs: complementary angles add to 90°, supplementary angles to 180°, and vertical angles are equal. Once the pair is named, most problems become a one-step or two-step equation.

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

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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.

  1. Solve with complementary angles

    Find the missing angle.56°x
  2. An angle measures 15∘. Find its complement.
  3. Find the complement of a 77∘ angle.
  4. Find the complement.64°x

  1. Solve with supplementary angles

    An angle measures 29∘. Find its supplement.
  2. The angles are supplementary. Find the unknown angle.x49°
  3. Two angles are supplementary. One measures 6∘. Find the other.
  4. Find the supplement of a 26∘ angle.

  1. Find angles in a given ratio

    Two supplementary angles are in the ratio 1:2. Find the smaller one.
  2. The angles are complementary. Find the larger angle.3x2x
  3. A right angle is split into two angles in the ratio 1:9. Find the larger angle.

  1. Name the angle relationship

    Give the most specific name. Two lines cross. ∠1 and ∠2 are across from each other.
  2. Give the most specific name. m∠1=61∘ and m∠2=29∘. They do not share a side.
  3. Give the most specific name. ∠1 and ∠2 share a vertex and a side, and their other sides form a straight line.

  1. Find angles around a point

    The angles fill the space all the way around the point. What is x?5x°6x°9x°
  2. Several rays start at one point. Solve for x.98°x°102°106°
  3. Together the marked angles go once around the point. Find x.40°223°(4x + 49)°

  1. Find angles where three lines meet

    Three straight lines pass through the same point. Find x.(5x − 36)°(x + 20)°
  2. The lines cross at one point, making six angles. Find x.99°44°(2x + 15)°
  3. Three straight lines pass through the same point. What is x?45°x°67°

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Angle RelationshipsAnswer keyVersion 2

Date Period

Find each angle, or name each relationship.

  1. Solve with complementary angles

    Find the missing angle.56°x34∘
  2. An angle measures 15∘. Find its complement.75∘
  3. Find the complement of a 77∘ angle.13∘
  4. Find the complement.64°x26∘

  1. Solve with supplementary angles

    An angle measures 29∘. Find its supplement.151∘
  2. The angles are supplementary. Find the unknown angle.x49°131∘
  3. Two angles are supplementary. One measures 6∘. Find the other.174∘
  4. Find the supplement of a 26∘ angle.154∘

  1. Find angles in a given ratio

    Two supplementary angles are in the ratio 1:2. Find the smaller one.60∘
  2. The angles are complementary. Find the larger angle.3x2x54∘
  3. A right angle is split into two angles in the ratio 1:9. Find the larger angle.81∘

  1. Name the angle relationship

    Give the most specific name. Two lines cross. ∠1 and ∠2 are across from each other.Vertical angles
  2. Give the most specific name. m∠1=61∘ and m∠2=29∘. They do not share a side.Complementary
  3. Give the most specific name. ∠1 and ∠2 share a vertex and a side, and their other sides form a straight line.Linear pair

  1. Find angles around a point

    The angles fill the space all the way around the point. What is x?5x°6x°9x°18
  2. Several rays start at one point. Solve for x.98°x°102°106°54
  3. Together the marked angles go once around the point. Find x.40°223°(4x + 49)°12

  1. Find angles where three lines meet

    Three straight lines pass through the same point. Find x.(5x − 36)°(x + 20)°14
  2. The lines cross at one point, making six angles. Find x.99°44°(2x + 15)°11
  3. Three straight lines pass through the same point. What is x?45°x°67°68

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Two complementary angles are in the ratio 2:3. Find the smaller one

  1. Complementary angles add to 90.
  2. The ratio has 2 + 3 = 5 parts, so each part is 90 ÷ 5 = 18.
  3. The smaller angle is 2 parts: 36.

The answer is 36∘.

Where students go wrong

Mixing up complementary and supplementary. Complementary makes a corner, 90°; supplementary makes a straight line, 180°.

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∘
Supplementary angles
The angles are supplementary. Find the unknown angle. — two angles, x and 101°, on a straight line → 79∘
Two angles in a ratio
Two supplementary angles are in the ratio 1:8. Find the smaller one. → 20∘
Name the relationship
Give the most specific name. m∠1=49∘ and m∠2=41∘. 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.

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 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.