Rule for Intersected Arc from Inscribed Angle (Level 1)

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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Geometry of Circles - Rule for Intersected Arc from Inscribed Angle Worksheet

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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/
1
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc MX compared to angle MZX?
a
MX and MZX add to 90º
b
MX is twice MZX
c
MX and MZX add to 360º
d
MX is the same as MZX
e
Nothing, MX and MZX are not subtended by the same arc
f
MX is half MZX
2
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc CX compared to angle CBX?
a
CX is twice CBX
b
CX is the same as CBX
c
CX is half CBX
d
CX and CBX add to 90º
e
CX and CBX add to 180º
f
Nothing, CX and CBX are not subtended by the same arc
3
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc DP compared to angle DRP?
a
DP is twice DRP
b
DP and DRP add to 180º
c
DP is half DRP
d
DP is the same as DRP
e
Nothing, DP and DRP are not subtended by the same arc
f
DP and DRP add to 90º
4
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc MX compared to angle MYX?
a
MX is twice MYX
b
Nothing, MX and MYX are not subtended by the same arc
c
MX and MYX add to 180º
d
MX is the same as MYX
e
MX and MYX add to 90º
f
MX is half MYX
5
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc ZD compared to angle ZPD?
a
ZD is the same as ZPD
b
ZD is half ZPD
c
ZD and ZPD add to 360º
d
Nothing, ZD and ZPD are not subtended by the same arc
e
ZD is twice ZPD
f
ZD and ZPD add to 90º
6
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc BP compared to angle BYP?
a
BP and BYP add to 360º
b
BP is twice BYP
c
BP is half BYP
d
BP and BYP add to 180º
e
BP is the same as BYP
f
BP and BYP add to 90º
7
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc XB compared to angle XDB?
a
XB is half XDB
b
Nothing, XB and XDB are not subtended by the same arc
c
XB is twice XDB
d
XB and XDB add to 180º
e
XB and XDB add to 360º
f
XB is the same as XDB