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Geometry practice

Arcs and Central Angles Worksheets

Name minor arcs, major arcs, semicircles and central angles, then find their measures with three or four points on a circle.

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Name the requested figures, then use the labeled central angles to find missing measures. A major arc and its smaller central angle have different measures.

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Follow the named path

A central angle matches its minor intercepted arc. A major arc takes the other path and measures 360 degrees minus the minor arc.

Learning objective

What this activity builds

Name arcs precisely and relate arc measures to central angles and the full 360-degree circle.

Worked example

The minor arc AB measures 76 degrees. What are the smaller central angle AOB and the major arc ACB?

Angle AOB = 76 degrees; major arc ACB = 284 degrees.

A smaller central angle has the same measure as its intercepted minor arc. The rest of the circle is 360 - 76 = 284 degrees.

Teaching notes

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  • Put the center letter in the middle of a central-angle name.
  • Use three letters to choose a major arc or one particular semicircle.
  • Account for all 360 degrees around the circle when finding a missing sector.

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Twelve tasks separate figure naming from measurement. Choose arcs, central angles, or both, and use three-point, four-point, or mixed measurement diagrams.

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Math SheetNameScoreTeacherDateArcs and Central AnglesName each marked figure or use the sector measures to find the requested arc and central angle.Name figures1.Name the marked minor arc and the central angle.OSTU2.Name the marked major arc and the central angle.ONPQ3.Name the marked semicircle arc and the central angle.OCDE4.Name the marked minor arc and the central angle.ORST5.Name the marked major arc and the central angle.OHJK6.Name the marked semicircle arc and the central angle.OUVWA central angle equals its intercepted arc; a major arc uses 360 degrees minus the minor arc.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateArcs and Central AnglesName each marked figure or use the sector measures to find the requested arc and central angle.Find measures7.Find minor arc ST and the central angle SOT.OSTUGiven: Angle TOU = 117 deg; Angle UOS = 180 deg.8.Find major arc TUS and the smaller central angle SOT.OSTUVGiven: Angle TOU = 79 deg; Angle UOV = 102 deg; Angle VOS = 128 deg.9.Find semicircle arc QRS and the central angle SOQ.OQRSGiven: Angle QOR = 63 deg; Angle ROS = 117 deg.10.Find minor arc MN and the central angle MON.OMNPQGiven: Angle NOP = 84 deg; Angle POQ = 102 deg; Angle QOM = 128 deg.11.Find major arc GHF and the smaller central angle FOG.OFGHGiven: Angle GOH = 113 deg; Angle HOF = 180 deg.12.Find semicircle arc JKM and the central angle MOJ.OJKLMGiven: Angle JOK = 51 deg; Angle KOL = 69 deg; Angle LOM = 60 deg.A central angle equals its intercepted arc; a major arc uses 360 degrees minus the minor arc.math-sheet.comPage 2 of 2

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