Geometry of Circles - Rule for Inscribed Angle from Intersected Arc (Level 1)

This math topic focuses on the geometric properties of circles, specifically the relationship between inscribed angles and the arcs they intersect. Students are required to apply and interpret the rule that an inscribed angle is half the measure of its intercepted arc, or variations of this rule. They are presented with diagrams of circles containing various points and arcs and are asked to compare the angular measurements of inscribed angles to the lengths of the corresponding arcs. Each problem presents multiple-choice answers, challenging students to distinguish correct relationships in the context of circle geometry.

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

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

Math worksheet on 'Geometry of Circles - Rule for Inscribed Angle from Intersected Arc (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 angle RPZ compared to the length (in degrees) of intersected arc RZ?

a

RZ and RPZ add to 360º

b

RPZ is half RZ

c

RZ is half RPZ

d

RZ is twice RPZ

e

RZ and RPZ add to 90º

f

RZ is the same as RPZ

2

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

a

ZR and ZYR add to 360º

b

ZR is the same as ZYR

c

ZR is twice ZYR

d

ZR is half ZYR

e

ZR and ZYR add to 90º

f

ZYR is half ZR

3

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

a

MZ is half MYZ

b

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

c

MZ and MYZ add to 180º

d

MZ is twice MYZ

e

MZ and MYZ add to 90º

f

MYZ is half MZ

4

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

a

BY and BDY add to 360º

b

Nothing, BY and BDY are not subtended by the same arc

c

BDY is half BY

d

BY and BDY add to 90º

e

BY is twice BDY

f

BY is the same as BDY

5

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

a

PB and PZB add to 180º

b

PZB is half PB

c

PB is twice PZB

d

PB is half PZB

e

Nothing, PB and PZB are not subtended by the same arc

f

PB and PZB add to 90º

6

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

a

RB is the same as RPB

b

RB and RPB add to 90º

c

RB and RPB add to 360º

d

RB is half RPB

e

RB and RPB add to 180º

f

RPB is half RB

7

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

a

YNB is half YB

b

YB is twice YNB

c

YB is the same as YNB

d

YB is half YNB

e

YB and YNB add to 90º

f

YB and YNB add to 180º