Geometry of Circles - 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.

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

Math worksheet on 'Geometry of Circles - Rule for Intersected Arc from Inscribed Angle (Level 1)'. Part of a broader unit on 'Geometry - Intermediate - Intro' Learn online: app.mobius.academy/math/units/geometry_intermediate_intro/

1

What is known about the length (in degrees) of intersected arc BC compared to angle BXC?

a

Nothing, BC and BXC are not subtended by the same arc

b

BC is twice BXC

c

BC is half BXC

d

BC and BXC add to 180º

e

BC is the same as BXC

f

BC and BXC add to 90º

2

What is known about the length (in degrees) of intersected arc RZ compared to angle RYZ?

a

RZ and RYZ add to 180º

b

RZ is twice RYZ

c

RZ is the same as RYZ

d

RZ and RYZ add to 90º

e

RZ and RYZ add to 360º

f

Nothing, RZ and RYZ are not subtended by the same arc

3

What is known about the length (in degrees) of intersected arc MZ compared to angle MPZ?

a

MZ is twice MPZ

b

MZ and MPZ add to 180º

c

MZ and MPZ add to 90º

d

MZ is half MPZ

e

MZ and MPZ add to 360º

f

Nothing, MZ and MPZ are not subtended by the same arc

4

What is known about the length (in degrees) of intersected arc RP compared to angle RZP?

a

RP and RZP add to 180º

b

Nothing, RP and RZP are not subtended by the same arc

c

RP is the same as RZP

d

RP and RZP add to 90º

e

RP is twice RZP

f

RP is half RZP

5

What is known about the length (in degrees) of intersected arc CZ compared to angle CDZ?

a

Nothing, CZ and CDZ are not subtended by the same arc

b

CZ is the same as CDZ

c

CZ and CDZ add to 90º

d

CZ and CDZ add to 180º

e

CZ is twice CDZ

f

CZ and CDZ add to 360º

6

What is known about the length (in degrees) of intersected arc RP compared to angle RMP?

a

RP and RMP add to 180º

b

RP is half RMP

c

RP and RMP add to 360º

d

RP is twice RMP

e

Nothing, RP and RMP are not subtended by the same arc

f

RP and RMP add to 90º

7

What is known about the length (in degrees) of intersected arc ZY compared to angle ZPY?

a

ZY and ZPY add to 90º

b

ZY is twice ZPY

c

Nothing, ZY and ZPY are not subtended by the same arc

d

ZY is the same as ZPY

e

ZY is half ZPY

f

ZY and ZPY add to 360º