Rule for Intersected Arc from Inscribed Angle (Level 1)

This math topic focuses on the relationships between angles and arcs in circle geometry. Specifically, it explores the rules governing the lengths of intersected arcs relative to inscribed angles. Problems are designed to assess understanding of how arc measures compare to the angles subtending them, including direct equality, halves, doubles, and their additive complements to 90°, 180°, and 360°. Each question presents a different configuration within a circle, requiring analysis of arcs and angles to determine their mathematical relationship.

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

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

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Geometry of Circles - Rule for Intersected Arc from Inscribed Angle
1
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc XB compared to angle XDB?
a
Nothing, XB and XDB are not subtended by the same arc
b
XB is half XDB
c
XB is the same as XDB
d
XB and XDB add to 180º
e
XB is twice XDB
f
XB and XDB add to 360º
2
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc PY compared to angle PDY?
a
PY is twice PDY
b
Nothing, PY and PDY are not subtended by the same arc
c
PY is the same as PDY
d
PY and PDY add to 180º
e
PY and PDY add to 90º
f
PY and PDY add to 360º
3
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc ZN compared to angle ZBN?
a
Nothing, ZN and ZBN are not subtended by the same arc
b
ZN is the same as ZBN
c
ZN and ZBN add to 180º
d
ZN is half ZBN
e
ZN and ZBN add to 90º
f
ZN is twice ZBN
4
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc CZ compared to angle CYZ?
a
CZ is twice CYZ
b
CZ is the same as CYZ
c
Nothing, CZ and CYZ are not subtended by the same arc
d
CZ and CYZ add to 90º
e
CZ and CYZ add to 180º
f
CZ and CYZ add to 360º
5
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc NB compared to angle NCB?
a
NB is the same as NCB
b
Nothing, NB and NCB are not subtended by the same arc
c
NB and NCB add to 360º
d
NB is half NCB
e
NB is twice NCB
f
NB and NCB add to 90º
6
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc NM compared to angle NYM?
a
NM is half NYM
b
NM and NYM add to 90º
c
NM and NYM add to 360º
d
NM is the same as NYM
e
NM is twice NYM
f
NM and NYM add to 180º
7
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc XY compared to angle XBY?
a
XY is the same as XBY
b
Nothing, XY and XBY are not subtended by the same arc
c
XY and XBY add to 180º
d
XY and XBY add to 90º
e
XY is half XBY
f
XY is twice XBY
8
An svg image showing a math problem
What is known about the length (in degrees) of intersected arc CX compared to angle CBX?
a
CX and CBX add to 90º
b
CX is the same as CBX
c
Nothing, CX and CBX are not subtended by the same arc
d
CX and CBX add to 180º
e
CX is twice CBX
f
CX is half CBX