This math topic focuses on the relationships between angles and arcs in circle geometry. Specifically, it explores the rules governing the lengths of intersected arcs relative to inscribed angles. Problems are designed to assess understanding of how arc measures compare to the angles subtending them, including direct equality, halves, doubles, and their additive complements to 90°, 180°, and 360°. Each question presents a different configuration within a circle, requiring analysis of arcs and angles to determine their mathematical relationship.
Work on practice problems directly here, or download the printable pdf worksheet to practice offline.
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Rule for Intersected Arc from Inscribed Angle
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What is known about the length (in degrees) of intersected arc DC compared to angle DZC?
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Geometry of Circles - Rule for Intersected Arc from Inscribed Angle Worksheet
| Math worksheet on 'Geometry of Circles - Rule for Intersected Arc from Inscribed Angle (Level 1)'. Part of a broader unit on 'Geometry - Intermediate - Intro' Learn online: app.mobius.academy/math/units/geometry_intermediate_intro/ |
| What is known about the length (in degrees) of intersected arc CB compared to angle CXB? |
| Nothing, CB and CXB are not subtended by the same arc |
| CB and CXB add to 360º |
| CB is half CXB |
| CB and CXB add to 90º |
| CB and CXB add to 180º |
| CB is twice CXB |
| What is known about the length (in degrees) of intersected arc MR compared to angle MZR? |
| MR is half MZR |
| MR is twice MZR |
| Nothing, MR and MZR are not subtended by the same arc |
| MR and MZR add to 180º |
| MR is the same as MZR |
| MR and MZR add to 360º |
| What is known about the length (in degrees) of intersected arc ZY compared to angle ZPY? |
| Nothing, ZY and ZPY are not subtended by the same arc |
| ZY and ZPY add to 90º |
| ZY is half ZPY |
| ZY is the same as ZPY |
| ZY and ZPY add to 360º |
| ZY is twice ZPY |
| What is known about the length (in degrees) of intersected arc DP compared to angle DZP? |
| DP and DZP add to 90º |
| DP and DZP add to 180º |
| DP and DZP add to 360º |
| DP is half DZP |
| DP is twice DZP |
| DP is the same as DZP |
| What is known about the length (in degrees) of intersected arc ZR compared to angle ZBR? |
| ZR and ZBR add to 90º |
| ZR and ZBR add to 360º |
| ZR is twice ZBR |
| ZR is the same as ZBR |
| ZR and ZBR add to 180º |
| ZR is half ZBR |
| What is known about the length (in degrees) of intersected arc DZ compared to angle DXZ? |
| DZ and DXZ add to 90º |
| DZ is the same as DXZ |
| DZ is half DXZ |
| Nothing, DZ and DXZ are not subtended by the same arc |
| DZ is twice DXZ |
| DZ and DXZ add to 360º |
| What is known about the length (in degrees) of intersected arc BC compared to angle BRC? |
| BC and BRC add to 90º |
| BC is twice BRC |
| Nothing, BC and BRC are not subtended by the same arc |
| BC is the same as BRC |
| BC and BRC add to 180º |
| BC is half BRC |