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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Math worksheet on 'Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle Rule (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 angle PXM and PMX given that XM forms a diameter?
a
PXM is half PMX
b
PXM and PMX add to 90º
c
PXM and PMX add to 180º
d
PXM is the same as PMX
e
Nothing, PXM and PMX are not subtended by the same arc
f
PXM and PMX add to 360º
2
An svg image showing a math problem
What is known about angle MRC and MCR given that RC forms a diameter?
a
MRC is the same as MCR
b
MRC and MCR add to 360º
c
MRC is half MCR
d
MRC and MCR add to 90º
e
MRC and MCR add to 180º
f
Nothing, MRC and MCR are not subtended by the same arc
3
An svg image showing a math problem
What is known about angle MXN and MNX given that XN forms a diameter?
a
MXN is twice MNX
b
MXN and MNX add to 90º
c
Nothing, MXN and MNX are not subtended by the same arc
d
MXN and MNX add to 180º
e
MXN is the same as MNX
f
MXN and MNX add to 360º
4
An svg image showing a math problem
What is known about angle DXR and DRX given that XR forms a diameter?
a
DXR and DRX add to 90º
b
Nothing, DXR and DRX are not subtended by the same arc
c
DXR and DRX add to 360º
d
DXR is half DRX
e
DXR is twice DRX
f
DXR and DRX add to 180º
5
An svg image showing a math problem
What is known about angle BYP and BPY given that YP forms a diameter?
a
BYP is the same as BPY
b
BYP is half BPY
c
BYP and BPY add to 180º
d
BYP is twice BPY
e
BYP and BPY add to 90º
f
Nothing, BYP and BPY are not subtended by the same arc
6
An svg image showing a math problem
What is known about angle ZBN and ZNB given that BN forms a diameter?
a
ZBN is twice ZNB
b
ZBN is the same as ZNB
c
ZBN is half ZNB
d
ZBN and ZNB add to 90º
e
ZBN and ZNB add to 180º
f
ZBN and ZNB add to 360º
7
An svg image showing a math problem
What is known about angle BRN and BNR given that RN forms a diameter?
a
BRN and BNR add to 90º
b
BRN and BNR add to 360º
c
BRN is twice BNR
d
BRN is half BNR
e
Nothing, BRN and BNR are not subtended by the same arc
f
BRN and BNR add to 180º