Rule for Inscribed Angle from Intersected Arc (Level 1)

This math topic focuses on the geometric properties of circles, specifically the relationship between inscribed angles and the arcs they intersect. Students are required to apply and interpret the rule that an inscribed angle is half the measure of its intercepted arc, or variations of this rule. They are presented with diagrams of circles containing various points and arcs and are asked to compare the angular measurements of inscribed angles to the lengths of the corresponding arcs. Each problem presents multiple-choice answers, challenging students to distinguish correct relationships in the context of circle geometry.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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

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Geometry of Circles - Rule for Inscribed Angle from Intersected Arc
1
An svg image showing a math problem
What is known about angle BRP compared to the length (in degrees) of intersected arc BP?
a
BP and BRP add to 180º
b
Nothing, BP and BRP are not subtended by the same arc
c
BP and BRP add to 90º
d
BP is twice BRP
e
BRP is half BP
f
BP and BRP add to 360º
2
An svg image showing a math problem
What is known about angle RMB compared to the length (in degrees) of intersected arc RB?
a
Nothing, RB and RMB are not subtended by the same arc
b
RMB is half RB
c
RB is half RMB
d
RB is the same as RMB
e
RB is twice RMB
f
RB and RMB add to 360º
3
An svg image showing a math problem
What is known about angle XRY compared to the length (in degrees) of intersected arc XY?
a
Nothing, XY and XRY are not subtended by the same arc
b
XY is the same as XRY
c
XY and XRY add to 180º
d
XRY is half XY
e
XY and XRY add to 360º
f
XY is twice XRY
4
An svg image showing a math problem
What is known about angle CXP compared to the length (in degrees) of intersected arc CP?
a
CP is half CXP
b
CP and CXP add to 360º
c
CP and CXP add to 180º
d
CP is twice CXP
e
CP and CXP add to 90º
f
CXP is half CP
5
An svg image showing a math problem
What is known about angle DXN compared to the length (in degrees) of intersected arc DN?
a
Nothing, DN and DXN are not subtended by the same arc
b
DN and DXN add to 180º
c
DXN is half DN
d
DN is twice DXN
e
DN is half DXN
f
DN is the same as DXN
6
An svg image showing a math problem
What is known about angle YCM compared to the length (in degrees) of intersected arc YM?
a
Nothing, YM and YCM are not subtended by the same arc
b
YM is half YCM
c
YM and YCM add to 180º
d
YCM is half YM
e
YM is the same as YCM
f
YM and YCM add to 360º
7
An svg image showing a math problem
What is known about angle PND compared to the length (in degrees) of intersected arc PD?
a
PD and PND add to 360º
b
PD is twice PND
c
PD and PND add to 90º
d
PD is the same as PND
e
PND is half PD
f
Nothing, PD and PND are not subtended by the same arc
8
An svg image showing a math problem
What is known about angle NDX compared to the length (in degrees) of intersected arc NX?
a
Nothing, NX and NDX are not subtended by the same arc
b
NX is twice NDX
c
NX and NDX add to 90º
d
NDX is half NX
e
NX is the same as NDX
f
NX and NDX add to 180º