Worksheets · Geometry

Angle bisectors worksheet

A bisector cuts an angle into two equal halves. So either half is the whole angle divided by two, the whole is either half doubled, and when the two halves are given as expressions they are equal to each other.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Angle Bisectors

Date Period

Find each measure.

  1.  extRayBD extbisectsABC ext.Findx8x - 503x + 15BADC
  2.  extRayBD extbisectsABC ext.Findx8x - 905x - 39BADC
  3.  extRayBD extbisectsABC ext.Findx3x + 55x - 21BADC
  4.  extRayBD extbisectsABC ext.FindABC70°70°BADC
  5.  extRayBD extbisectsABC ext.FindABC44°44°BADC
  6.  extRayBD extbisectsABC ext.Findx6x - 545x - 40BADC
  7.  extRayBD extbisectsABC ext.Findx5x - 27x - 30BADC
  8.  extRayBD extbisectsABC ext.Findx3x + 294x + 15BADC
  9.  extRayBD extbisectsABC ext.Findx7x - 726x - 58BADC
  10.  extRayBD extbisectsABC ext.FindABC14°14°BADC
  11.  extRayBD extbisectsABC ext.Findx7x - 104x + 32BADC
  12.  extRayBD extbisectsABC ext.FindABC85°85°BADC
  13.  extRayBD extbisectsABC ext.Findx8x - 682x + 40BADC
  14.  extRayBD extbisectsABC ext.FindABC33°33°BADC
  15.  extRayBD extbisectsABC ext.Findx3x + 136x - 41BADC
  16.  extRayBD extbisectsABC ext.Findx3x + 484x + 35BADC
  17.  extRayBD extbisectsABC ext.FindABC36°36°BADC
  18.  extRayBD extbisectsABC ext.Findx7x - 923x - 28BADC
  19.  extRayBD extbisectsABC ext.FindABC80°80°BADC
  20.  extRayBD extbisectsABC ext.FindABC53°53°BADC

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

Sigma Prep · sigmaprep.io/worksheets

Name

Angle BisectorsAnswer keyVersion 1

Date Period

Find each measure.

  1.  extRayBD extbisectsABC ext.Findx8x - 503x + 15BADC13
  2.  extRayBD extbisectsABC ext.Findx8x - 905x - 39BADC17
  3.  extRayBD extbisectsABC ext.Findx3x + 55x - 21BADC13
  4.  extRayBD extbisectsABC ext.FindABC70°70°BADC140
  5.  extRayBD extbisectsABC ext.FindABC44°44°BADC88
  6.  extRayBD extbisectsABC ext.Findx6x - 545x - 40BADC14
  7.  extRayBD extbisectsABC ext.Findx5x - 27x - 30BADC14
  8.  extRayBD extbisectsABC ext.Findx3x + 294x + 15BADC14
  9.  extRayBD extbisectsABC ext.Findx7x - 726x - 58BADC14
  10.  extRayBD extbisectsABC ext.FindABC14°14°BADC28
  11.  extRayBD extbisectsABC ext.Findx7x - 104x + 32BADC14
  12.  extRayBD extbisectsABC ext.FindABC85°85°BADC170
  13.  extRayBD extbisectsABC ext.Findx8x - 682x + 40BADC18
  14.  extRayBD extbisectsABC ext.FindABC33°33°BADC66
  15.  extRayBD extbisectsABC ext.Findx3x + 136x - 41BADC18
  16.  extRayBD extbisectsABC ext.Findx3x + 484x + 35BADC13
  17.  extRayBD extbisectsABC ext.FindABC36°36°BADC72
  18.  extRayBD extbisectsABC ext.Findx7x - 923x - 28BADC16
  19.  extRayBD extbisectsABC ext.FindABC80°80°BADC160
  20.  extRayBD extbisectsABC ext.FindABC53°53°BADC106

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

How to do these

Ray BD bisects ABC. If ABD=42, find ABC

  1. ABD is half of the whole angle.
  2. So the whole is twice 42.

The answer is 84.

Where students go wrong

Halving when you should double. If you are given one of the halves, the whole angle is bigger, not smaller. Check which one the question names before dividing.

Also called bisecting an angle or angle bisector.

Questions about these worksheets

Yes. Every angle bisectors 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 bisectors 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.

Halving when you should double. If you are given one of the halves, the whole angle is bigger, not smaller. Check which one the question names before dividing.