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Angles at the Centre and Circumference of a Circle

In this worksheet, students resolve problems with angles at the centre and circumference of a circle.

'Angles at the Centre and Circumference of a Circle' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Identify and Apply Circle Definitions and Properties

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about calculating angles at the centre and circumference of a circle.

 

Angle Rules

 


1) Angles in the same segment, on the same chord, are equal at the circumference.

2) The angle on the circumference on a semicircle, on any diameter is a right angle.

3) The angle at the centre is twice the angle at the circumference (from the same chord).

 

Example

Find the angle marked x in this diagram.


a = 39
x = ____

 

Answer

x is half of a, according to rule 3 above.

x = 39 ÷ 2 = 19.5 degrees

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 72
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 35
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 14
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 24
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 111
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 116
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 29
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 116
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 41
x = ____

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 39
x = ____

  • Question 1

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 72
x = ____

CORRECT ANSWER
36
EDDIE SAYS
x is half of a
  • Question 2

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 35
x = ____

CORRECT ANSWER
35
EDDIE SAYS
x and a are equal angles
  • Question 3

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 14
x = ____

CORRECT ANSWER
14
EDDIE SAYS
x and a are equal angles
  • Question 4

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 24
x = ____

CORRECT ANSWER
24
EDDIE SAYS
x and a are equal angles
  • Question 5

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 111
x = ____

CORRECT ANSWER
55.5
EDDIE SAYS
x is half of a
  • Question 6

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 116
x = ____

CORRECT ANSWER
58
EDDIE SAYS
x is half of a
  • Question 7

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 29
x = ____

CORRECT ANSWER
29
EDDIE SAYS
x and a are equal angles
  • Question 8

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 116
x = ____

CORRECT ANSWER
58
EDDIE SAYS
x is half of a
  • Question 9

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)

 


a = 41
x = ____

CORRECT ANSWER
20.5
EDDIE SAYS
x is half of a
  • Question 10

Find the angle marked x in this diagram.  All angles shown are in degrees.

(Just write the number)


a = 39
x = ____

CORRECT ANSWER
19.5
EDDIE SAYS
x is half of a
---- OR ----

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