Inscribed Angles Subtended by Same Arc - Rule (Level 1)

This math topic covers the geometric properties of inscribed angles in circles, specifically focusing on inscribed angles subtended by the same arc. Problems delve into the relationships and measurements between various pairs of angles that share an arc, examining whether they are equal to, the sum of, half of, twice, or unrelated to each other. The learners are asked to identify these relationships through a series of multiple-choice questions, enhancing their understanding of how arcs and angles in circles interact.

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

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Geometry of Circles - Inscribed Angles Subtended by Same Arc - Rule Worksheet

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Geometry of Circles - Inscribed Angles Subtended by Same Arc - Rule
1
An svg image showing a math problem
What is known about angle DNC and DXC given that they are both subtended by arc DC?
a
DNC is the same as DXC
b
DNC and DXC add to 180º
c
Nothing, DNC and DXC are not subtended by the same arc
d
DNC is twice DXC
e
DNC is half DXC
f
DNC and DXC add to 90º
2
An svg image showing a math problem
What is known about angle YMP and YNP given that they are both subtended by arc YP?
a
YMP and YNP add to 90º
b
YMP and YNP add to 180º
c
Nothing, YMP and YNP are not subtended by the same arc
d
YMP is twice YNP
e
YMP is half YNP
f
YMP is the same as YNP
3
An svg image showing a math problem
What is known about angle XMP and XNP given that they are both subtended by arc XP?
a
XMP and XNP add to 360º
b
XMP and XNP add to 90º
c
Nothing, XMP and XNP are not subtended by the same arc
d
XMP and XNP add to 180º
e
XMP is the same as XNP
f
XMP is twice XNP
4
An svg image showing a math problem
What is known about angle RYC and RBC given that they are both subtended by arc RC?
a
RYC and RBC add to 360º
b
RYC is twice RBC
c
RYC and RBC add to 180º
d
RYC and RBC add to 90º
e
Nothing, RYC and RBC are not subtended by the same arc
f
RYC is the same as RBC
5
An svg image showing a math problem
What is known about angle YBX and YZX given that they are both subtended by arc YX?
a
YBX and YZX add to 180º
b
Nothing, YBX and YZX are not subtended by the same arc
c
YBX is the same as YZX
d
YBX is twice YZX
e
YBX and YZX add to 90º
f
YBX and YZX add to 360º
6
An svg image showing a math problem
What is known about angle ZPM and ZCM given that they are both subtended by arc ZM?
a
ZPM is the same as ZCM
b
ZPM and ZCM add to 360º
c
ZPM is half ZCM
d
ZPM and ZCM add to 90º
e
ZPM and ZCM add to 180º
f
Nothing, ZPM and ZCM are not subtended by the same arc
7
An svg image showing a math problem
What is known about angle PYR and PXR given that they are both subtended by arc PR?
a
PYR is twice PXR
b
PYR and PXR add to 360º
c
PYR and PXR add to 90º
d
PYR is half PXR
e
PYR and PXR add to 180º
f
PYR is the same as PXR
8
An svg image showing a math problem
What is known about angle PRB and PZB given that they are both subtended by arc PB?
a
PRB is twice PZB
b
PRB is half PZB
c
PRB and PZB add to 90º
d
PRB is the same as PZB
e
PRB and PZB add to 180º
f
PRB and PZB add to 360º