Tangent Triangle with Missing Angle - Rule (Level 1)

This math topic involves solving problems related to the geometry of circles, particularly focusing on tangent triangles and the properties of angles formed when lines tangent to circles intersect such triangles. Students are required to determine relationships between angles, possibly using concepts like supplementary and complementary angles, and equal angles subtended by the same arc. This enhances their understanding of geometric properties and angle calculations in the context of circles and tangents at an intermediate level.

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

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Geometry of Circles - Tangent Triangle with Missing Angle - Rule Worksheet

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Geometry of Circles - Tangent Triangle with Missing Angle - Rule
1
An svg image showing a math problem
What is known about angle XCY and XYC given that PY forms a tangent?
a
XCY is half XYC
b
XCY is the same as XYC
c
XCY and XYC add to 360º
d
XCY and XYC add to 180º
e
XCY and XYC add to 90º
f
XCY is twice XYC
2
An svg image showing a math problem
What is known about angle YDZ and YZD given that XZ forms a tangent?
a
YDZ is half YZD
b
YDZ and YZD add to 90º
c
YDZ is twice YZD
d
YDZ and YZD add to 180º
e
Nothing, YDZ and YZD are not subtended by the same arc
f
YDZ is the same as YZD
3
An svg image showing a math problem
What is known about angle MRX and MXR given that PX forms a tangent?
a
MRX is half MXR
b
MRX and MXR add to 360º
c
MRX is twice MXR
d
MRX and MXR add to 180º
e
MRX and MXR add to 90º
f
MRX is the same as MXR
4
An svg image showing a math problem
What is known about angle CYX and CXY given that BX forms a tangent?
a
CYX is the same as CXY
b
CYX and CXY add to 180º
c
CYX is half CXY
d
CYX and CXY add to 360º
e
CYX and CXY add to 90º
f
CYX is twice CXY
5
An svg image showing a math problem
What is known about angle ZBR and ZRB given that CR forms a tangent?
a
ZBR and ZRB add to 90º
b
ZBR and ZRB add to 360º
c
ZBR is the same as ZRB
d
ZBR and ZRB add to 180º
e
ZBR is half ZRB
f
Nothing, ZBR and ZRB are not subtended by the same arc
6
An svg image showing a math problem
What is known about angle NXM and NMX given that RM forms a tangent?
a
NXM and NMX add to 360º
b
NXM is the same as NMX
c
Nothing, NXM and NMX are not subtended by the same arc
d
NXM and NMX add to 90º
e
NXM is half NMX
f
NXM and NMX add to 180º
7
An svg image showing a math problem
What is known about angle BRZ and BZR given that PZ forms a tangent?
a
BRZ is half BZR
b
BRZ is twice BZR
c
BRZ and BZR add to 360º
d
BRZ and BZR add to 90º
e
BRZ and BZR add to 180º
f
BRZ is the same as BZR
8
An svg image showing a math problem
What is known about angle CPR and CRP given that NR forms a tangent?
a
CPR and CRP add to 90º
b
CPR is the same as CRP
c
CPR is twice CRP
d
CPR and CRP add to 360º
e
CPR is half CRP
f
Nothing, CPR and CRP are not subtended by the same arc