Inscribed Triangle on Diameter - Missing Angle Rule (Level 1)

This math topic focuses on the geometry of circles, specifically problems involving inscribed triangles with diameters and the relationships of their angles. Students are tasked with determining properties and relationships of angles subtended by diameters in various geometric configurations. The topic also challenges learners to deepen their understanding of the circle geometry, including how angles in inscribed triangles relate to one another and the circle's diameter. Each problem presents different cases of inscribed angles and related angle properties, crucial for learning intermediate level geometry.

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

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Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle Rule Worksheet

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Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle Rule
1
An svg image showing a math problem
What is known about angle MDB and MBD given that DB forms a diameter?
a
MDB is the same as MBD
b
MDB is twice MBD
c
Nothing, MDB and MBD are not subtended by the same arc
d
MDB is half MBD
e
MDB and MBD add to 90º
f
MDB and MBD add to 360º
2
An svg image showing a math problem
What is known about angle ZXC and ZCX given that XC forms a diameter?
a
ZXC and ZCX add to 90º
b
Nothing, ZXC and ZCX are not subtended by the same arc
c
ZXC is half ZCX
d
ZXC is the same as ZCX
e
ZXC and ZCX add to 180º
f
ZXC and ZCX add to 360º
3
An svg image showing a math problem
What is known about angle BNP and BPN given that NP forms a diameter?
a
BNP is half BPN
b
BNP and BPN add to 90º
c
Nothing, BNP and BPN are not subtended by the same arc
d
BNP is twice BPN
e
BNP is the same as BPN
f
BNP and BPN add to 360º
4
An svg image showing a math problem
What is known about angle RDX and RXD given that DX forms a diameter?
a
RDX is the same as RXD
b
RDX and RXD add to 360º
c
RDX is twice RXD
d
RDX is half RXD
e
RDX and RXD add to 90º
f
Nothing, RDX and RXD are not subtended by the same arc
5
An svg image showing a math problem
What is known about angle PNX and PXN given that NX forms a diameter?
a
PNX and PXN add to 90º
b
PNX is the same as PXN
c
PNX and PXN add to 180º
d
PNX is half PXN
e
Nothing, PNX and PXN are not subtended by the same arc
f
PNX is twice PXN
6
An svg image showing a math problem
What is known about angle PNX and PXN given that NX forms a diameter?
a
PNX is half PXN
b
PNX is the same as PXN
c
PNX and PXN add to 90º
d
PNX and PXN add to 180º
e
Nothing, PNX and PXN are not subtended by the same arc
f
PNX is twice PXN
7
An svg image showing a math problem
What is known about angle BYP and BPY given that YP forms a diameter?
a
BYP and BPY add to 180º
b
BYP is the same as BPY
c
BYP and BPY add to 90º
d
Nothing, BYP and BPY are not subtended by the same arc
e
BYP is twice BPY
f
BYP is half BPY
8
An svg image showing a math problem
What is known about angle PXM and PMX given that XM forms a diameter?
a
PXM is the same as PMX
b
PXM and PMX add to 180º
c
PXM is half PMX
d
PXM and PMX add to 360º
e
Nothing, PXM and PMX are not subtended by the same arc
f
PXM and PMX add to 90º