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Inscribed Angles Worksheets

Name inscribed angles and intercepted arcs, then solve angle, triangle and cyclic quadrilateral problems with worked answer keys.

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Name the requested angle and arc. For measures, identify the intercepted arc opposite the vertex before choosing a rule.

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A4

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Look opposite the vertex

An inscribed angle has its vertex on the circle and measures half its intercepted arc.

Learning objective

What this activity builds

Use the inscribed-angle theorem and triangle or cyclic quadrilateral angle rules.

Worked example

Angle ABC is inscribed in a circle and intercepts arc ADC measuring 126 degrees. Find angle ABC.

63 degrees.

The intercepted arc does not contain vertex B. An inscribed angle measures half that arc: 126 / 2 = 63 degrees.

Teaching notes

Make the practice count

  • The vertex of an inscribed angle lies on the circle.
  • Use the intercepted arc that does not contain the angle vertex.
  • Triangle angles total 180 degrees; opposite angles of a cyclic quadrilateral also total 180 degrees.

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Twelve tasks cover naming, missing angles, and intercepted arcs. Angle, triangle, and cyclic quadrilateral figures can be selected independently.

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Math SheetNameScoreTeacherDateInscribed AnglesName inscribed figures and use circle theorems to find missing angle or intercepted arc measures.Name figures1.Name the marked inscribed angle and its intercepted arc.ORSTU2.Name the marked inscribed angle and its intercepted arc.ONPQR3.Name the marked inscribed angle and its intercepted arc.ORSTU4.Name the marked inscribed angle and its intercepted arc.OBCDEAn inscribed angle is half its intercepted arc.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateInscribed AnglesName inscribed figures and use circle theorems to find missing angle or intercepted arc measures.Find angle measures5.Intercepted arc PQR = 86 deg. Find angle PSR.OPQRS6.The intercepted arc at vertex S is 72 deg and angle N is 34 deg. Find angleQ.ONPQRST7.Angle E = 96 deg. Find opposite angle J.OEFGHJKLM8.Intercepted arc DEF = 180 deg. Find angle DGF.ODEFGAn inscribed angle is half its intercepted arc.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateInscribed AnglesName inscribed figures and use circle theorems to find missing angle or intercepted arc measures.Find intercepted arc measures9.Angle LPN = 45 deg. Find intercepted arc LMN.OLMNP10.Angle ACY = 40 deg. Find intercepted arc YZA.OYZABCD11.Angle RTV = 72 deg. Find intercepted arc VPR.OPQRSTUVW12.Angle MQP = 90 deg. Find intercepted arc MNP.OMNPQAn inscribed angle is half its intercepted arc.math-sheet.comPage 3 of 3

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