Worksheets · Geometry

Angle addition postulate worksheet

If a ray runs inside an angle, it splits it into two angles that add up to the whole. The letters say which angle is which: the middle letter is always the vertex.

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Angle Addition Postulate

Date Period

Find each value asked for.

  1. Ray KZ is inside ∠SKL, and m∠SKL=93∘. Find xSZLKx + 108x − 7
  2. Point E is inside ∠NTS. m∠NTE=(3x−2)∘, m∠ETS=(3x−4)∘, m∠NTS=72∘. Find m∠ETSNEST
  3. Ray SN is inside ∠DSC, and m∠DSC=69∘. Find xDNCS2x + 23x − 3
  4. Point Y is inside ∠GRS. m∠GRY=(4x+12)∘, m∠YRS=(5x+7)∘, m∠GRS=64∘. Find m∠GRYGYSR
  5. Ray BG is inside ∠DBR, and m∠DBR=95∘. Find xDGRB3x − 75x − 2
  6. Point S is inside ∠ZHW. m∠ZHS=(6x−8)∘, m∠SHW=(5x−5)∘, m∠ZHW=141∘. Find m∠ZHSZSWH
  7. Ray FJ is inside ∠RFG, and m∠RFG=110∘. Find xRJGF3x + 48x + 7
  8. Point M is inside ∠HFT. m∠HFM=(5x+3)∘, m∠MFT=2x∘, m∠HFT=101∘. Find m∠MFTHMTF
  9. Ray RN is inside ∠GRY, and m∠GRY=108∘. Find xGNYR6x − 17x − 8
  10. Point J is inside ∠VCP. m∠VCJ=(5x+12)∘, m∠JCP=(2x+12)∘, m∠VCP=45∘. Find m∠VCJVJPC
  11. Ray AJ is inside ∠BAR, and m∠BAR=43∘. Find xBJRA5x − 26x + 1
  12. Point M is inside ∠AVN. m∠AVM=(4x−8)∘, m∠MVN=(4x+10)∘, m∠AVN=122∘. Find m∠MVNAMNV
  13. Ray UC is inside ∠WUE, and m∠WUE=108∘. Find xWCEU4x + 14x + 3
  14. Point K is inside ∠LPE. m∠LPK=(5x+11)∘, m∠KPE=(5x+9)∘, m∠LPE=80∘. Find m∠KPELKEP
  15. Ray JT is inside ∠WJS, and m∠WJS=143∘. Find xWTSJ5x + 55x + 8
  16. Point P is inside ∠CTU. m∠CTP=(6x+2)∘, m∠PTU=(2x+5)∘, m∠CTU=127∘. Find m∠CTPCPUT
  17. Ray GY is inside ∠BGJ, and m∠BGJ=149∘. Find xBYJG7x − 46x − 3
  18. Point Z is inside ∠YLP. m∠YLZ=(4x+1)∘, m∠ZLP=(4x−6)∘, m∠YLP=83∘. Find m∠YLZYZPL
  19. Ray AM is inside ∠FAL, and m∠FAL=129∘. Find xFMLA5x + 48x − 5
  20. Point R is inside ∠JZM. m∠JZR=(5x−5)∘, m∠RZM=(5x+3)∘, m∠JZM=68∘. Find m∠RZMJRMZ

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Angle Addition PostulateAnswer keyVersion 1

Date Period

Find each value asked for.

  1. Ray KZ is inside ∠SKL, and m∠SKL=93∘. Find xSZLKx + 108x − 7x=10
  2. Point E is inside ∠NTS. m∠NTE=(3x−2)∘, m∠ETS=(3x−4)∘, m∠NTS=72∘. Find m∠ETSNEST35∘
  3. Ray SN is inside ∠DSC, and m∠DSC=69∘. Find xDNCS2x + 23x − 3x=14
  4. Point Y is inside ∠GRS. m∠GRY=(4x+12)∘, m∠YRS=(5x+7)∘, m∠GRS=64∘. Find m∠GRYGYSR32∘
  5. Ray BG is inside ∠DBR, and m∠DBR=95∘. Find xDGRB3x − 75x − 2x=13
  6. Point S is inside ∠ZHW. m∠ZHS=(6x−8)∘, m∠SHW=(5x−5)∘, m∠ZHW=141∘. Find m∠ZHSZSWH76∘
  7. Ray FJ is inside ∠RFG, and m∠RFG=110∘. Find xRJGF3x + 48x + 7x=9
  8. Point M is inside ∠HFT. m∠HFM=(5x+3)∘, m∠MFT=2x∘, m∠HFT=101∘. Find m∠MFTHMTF28∘
  9. Ray RN is inside ∠GRY, and m∠GRY=108∘. Find xGNYR6x − 17x − 8x=9
  10. Point J is inside ∠VCP. m∠VCJ=(5x+12)∘, m∠JCP=(2x+12)∘, m∠VCP=45∘. Find m∠VCJVJPC27∘
  11. Ray AJ is inside ∠BAR, and m∠BAR=43∘. Find xBJRA5x − 26x + 1x=4
  12. Point M is inside ∠AVN. m∠AVM=(4x−8)∘, m∠MVN=(4x+10)∘, m∠AVN=122∘. Find m∠MVNAMNV70∘
  13. Ray UC is inside ∠WUE, and m∠WUE=108∘. Find xWCEU4x + 14x + 3x=13
  14. Point K is inside ∠LPE. m∠LPK=(5x+11)∘, m∠KPE=(5x+9)∘, m∠LPE=80∘. Find m∠KPELKEP39∘
  15. Ray JT is inside ∠WJS, and m∠WJS=143∘. Find xWTSJ5x + 55x + 8x=13
  16. Point P is inside ∠CTU. m∠CTP=(6x+2)∘, m∠PTU=(2x+5)∘, m∠CTU=127∘. Find m∠CTPCPUT92∘
  17. Ray GY is inside ∠BGJ, and m∠BGJ=149∘. Find xBYJG7x − 46x − 3x=12
  18. Point Z is inside ∠YLP. m∠YLZ=(4x+1)∘, m∠ZLP=(4x−6)∘, m∠YLP=83∘. Find m∠YLZYZPL45∘
  19. Ray AM is inside ∠FAL, and m∠FAL=129∘. Find xFMLA5x + 48x − 5x=10
  20. Point R is inside ∠JZM. m∠JZR=(5x−5)∘, m∠RZM=(5x+3)∘, m∠JZM=68∘. Find m∠RZMJRMZ38∘

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

How to do these

Point D is inside ∠ABC. m∠ABD=(2x+5)∘, m∠DBC=3x∘, m∠ABC=80∘. Find m∠ABD

  1. The two parts add to the whole: 2x + 5 plus 3x equals 80.
  2. 5x + 5 = 80, so x = 15.
  3. Put it back: 2(15) + 5 = 35.

The answer is 35∘.

Where students go wrong

Reading the angle from the wrong letters. In angle ABD the vertex is B, the middle letter, and the angle runs from ray BA round to ray BD.

Also called angle addition, angle addition postulate or adjacent angles find x.

What you can put on this worksheet

The angle addition postulate
Ray PT is inside ∠KPW, and m∠KPW=63∘. Find x — angle kpw with ray pt inside it, labeled K, T, W, P, 2x + 4, 5x − 4 → x=9
Find an angle, not just x
Point H is inside ∠FZV. m∠FZH=(4x−7)∘, m∠HZV=(3x+2)∘, m∠FZV=79∘. Find m∠HZV — angle fzv with ray zh inside it, labeled F, H, V, Z → 38∘

Questions about these worksheets

Yes. Every angle addition postulate 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 addition postulate 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 2: the angle addition postulate and find an angle, not just x. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading the angle from the wrong letters. In angle ABD the vertex is B, the middle letter, and the angle runs from ray BA round to ray BD.